1. Consider the function f(x) = x2 + 2x - 8.
(a) What are the x-intercepts of the graph of the function?
(b) What is the equation of the axis of symmetry? Explain how you know.
(c) What is the vertex of the function? Show your work.
(d) What is the domain of the function? Use set notation (i.e. { x | x > 1} )
(e) What is the range of the function? Use set notation (i.e. { y | y ≥ 1} )
(f) Graph the function.
Answers
ANSWER
a)The x-intercepts are:
(-4,0) and (2,0)
b) The axis of symmetry is x=-1
c) The vertex of this function is (-1,-9)
d)Domain: { [tex]x|x \in \: R[/tex]}
e) Range : {[tex]y |y \geqslant - 9[/tex]}
EXPLANATION
The given function is:
[tex]f(x) = {x}^{2} + 2x - 8[/tex]
We complete the square to write this function in the form:
[tex]f(x)=a{(x - h)}^{2} + k[/tex]
We add and subtract the square of half the coefficient of x.
[tex]f(x) = {x}^{2} + 2x + {1}^{2} - {1}^{2} - 8[/tex]
[tex]f(x) = {(x + 1)}^{2} - 9[/tex]
The vertex of this function is (h,k) which is (-1,-9)
The equation of axis of symmetry is x=h
But h=-1, hence the axis of symmetry isx=-1
To find the x-intercepts, we put f(x)=0
[tex]{(x + 1)}^{2} - 9 = 0[/tex]
[tex]{(x + 1)}^{2} = 9[/tex]
[tex]x + 1= \pm \sqrt{9} [/tex]
[tex]x= - 1 \pm3[/tex]
x=-4, 2
The x-intercepts are:
(-4,0) and (2,0)
The given function is a polynomial function, the domain is all real numbers.
[tex]x|x \in \: R[/tex]
e) The function has a minimum value of y=-9.
Therefore the range is
[tex]y |y \geqslant - 9[/tex]
Using the intercepts and vertex we can now draw this graph easily.
The graph of this function is shown in the attachment.
Final answer:
To address the student's question about the quadratic function, x-intercepts are found by setting the equation to zero, the axis of symmetry is calculated using -b/(2a), and the vertex is derived from these elements. The domain is all real numbers, and the range is all y-values greater than or equal to the y-value of the vertex. Finally, the function is graphically represented by plotting key points and drawing a parabola.
Explanation:
The student has inquired about the quadratic function f(x) = x2 + 2x - 8.
The x-intercepts of a quadratic function are the values of x where f(x) = 0. To find the x-intercepts, we set the equation to zero and solve for x: x2 + 2x - 8 = 0. In this case, the x-intercepts can be found using factorization or the quadratic formula.
The axis of symmetry is a vertical line that divides the parabola into two mirror images. For a quadratic function in the form of f(x) = ax2 + bx + c, the axis of symmetry equation is x = -b/(2a). We can use this formula to find the axis of symmetry for the given function.
The vertex of the function is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. To find the vertex, we use the axis of symmetry and plug that x-value into the function to find the corresponding y-value.
The domain of any quadratic function is all real numbers, which is denoted as {x | x is a real number}.
The range of a quadratic function depends on whether the parabola opens upwards or downwards. For the given function f(x) = x2 + 2x - 8, which opens upwards, the range is {y | y is greater than or equal to the y-value of the vertex}.
To graph the function, plot the vertex, axis of symmetry, and x-intercepts on a coordinate plane, then draw a smooth curve through these points to complete the parabola.
Related Questions
Having trouble to find the answer help plssssss
Answers
Answer:
it is 20
Step-by-step explanation:
5 * 20 = 100
100 - 10 = 90 which equals a angle in a right angle triangle
Answer:
The value of x is 11 ⇒ answer B
Step-by-step explanation:
* lets check the properties of the square
- Its four aides are equal
- Its four angles are equal and the measure of each one is 90°
- Its diagonals bisect its vertices
∵ BD is a diagonal of the square
∴ BD bisects angle B
∴ m∠ABD = m∠CBD
∵ B is a vertex of the square
∴ m∠B = 90°
∴ m∠ABD = m∠CBD = 90 ÷ 2 = 45°
∵ m∠ABD = (5x - 10)°
∴ (5x - 10)° = 45° ⇒ add 10 to each side
∴ 5x = 55 ⇒ divide both sides by 5
∴ x = 11
* The value of x is 11
Please help I will mark brainliest!!! (10 points)
Answers
Answer:
A: 700
B: 6400
C: 50
Step-by-step explanation:
A: You can multiply by 5
B: You can just multiply by 20.
C: Every 10% is 5, because 15(30%)/3 is 5. 5 times 10 is 50.
Answer:
a. h = 700
b. j = 6400
c. g = 50
Step-by-step explanation:
Translate each statement into an equation and solve the equation. Remember that to change a percent to a decimal, you divide the percent by 100, which is the same as moving the decimal point two places to the left. Also, a percent of a number means a percent times the number.
a. 20% of h is 140
20% * h = 140
0.2h = 140
Divide both sides by 0.2
h = 700
b. 5% of j is 320
5% * j = 320
0.05j = 320
Divide both sides by 0.05
j = 6400
c. 30% of g is 15
30% * g = 15
0.3g = 15
Divide both sides by 0.3
g = 50
What the equation of the quadratic function in standard form represented by the graph
Answers
Answer:
x^2 +6x +8
Step-by-step explanation:
The zeros of the graphed function appear to be (-4, 0) and (-2, 0). It appears the vertex is (-3, -1).
The standard form of the function with zeros p and q is ...
(x -p)(x -q) = x^2 -(p+q)x +pq
So, for zeros p=-4, q=-2, the standard form is ...
x^2 -(-4-2)x +(-4)(-2) = x^2 +6x +8
We can check to make sure the above vertex point satisfies this function:
(-3)^2 +6(-3) +8 = 9 -18 +8 = -1
The vertex satisfies the function we wrote, so there are no additional vertical scale factors required.
The function is ...
y = x^2 +6x +8
At the beginning of each school year, Madison Middle School orders new shirts for the entire student body. Each student receives
one shirt. Each shirt is the same price, s, and the school orders enough for n students. Which equation represents the
proportional relationship between P, the total price of the shirts, and the number of students?
NEED DONE NOW!!! WILL MARK BRAINLIEST
Answers
The equation representing the price of the shirt s, the number of students n and P is Option A.
sn = P
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of students be = n
Let the cost of each shirt be = s
The equation will be ,
So , the total cost of the shirt P = number of students x cost of each shirt
Total cost of the shirt P = n x s
So , the equation representing the proportional relationship is
P = ns
sn = P
Hence , The equation representing the price of the shirt s, the number of students n and P is Option A.
sn = P
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Sam worked 26 hours so far this week. He normally works a 40 hour week What fraction and percent represents the portion of hours he has worked? Simplify the fraction
Answers
Answer:
13/20, 65%
Step-by-step explanation:
So he has worked 26 hours out of 40 so that becomes 26/40 that is equal to 13/20 so that is your fraction and to convert to a percentage times 100 go that equals 65 so 65%
Use the Distributive Property to write each expression as an equivalent algebraic expression.
(7 + a)3
Answers
Answer:
21 + 3a
Step-by-step explanation:
3 (7+a)
distribute 3 into parentheses:
21 + 3a
The distributive property states that one should simplify the expression by multiplying each term inside the parentheses by the term outside of them:
3*7=21
3*a=3a
21+3a
Hope this helps!!
What is the value of tan B?
6/8
8/10
8/6
6/10
Answers
Answer:
8/6Step-by-step explanation:
[tex]tangent=\dfrac{opposite}{adjacent}\\\\\text{We have}\\\\opposite=8cm\\adjacent=6cm\\\\\text{substitute:}\\\\\tan B=\dfrac{8}{6}=\dfrac{8:2}{6:2}=\dfrac{4}{3}[/tex]
Ron is slicing 5 pizzas each pizza slice is 1/8 of the pizza. How many pizza slices will be there in all
Answers
Answer:
there would be 40 slices of pizza
Step-by-step explanation:
If 5 pizzas each have 8 slices you multiply 5 X 8 which equals 40 slices
Answer:
there would be 40 slices of pizza.
Step-by-step explanation:
25. Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not drawn to scale.
please answer ASAP if you have the answers for the whole exam I'll take them to please
A.48cm^2
B.40cm^2
C.32cm^2
D.44cm^2
Answers
Answer:
Option D. [tex]44\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}[b1+b2]h[/tex]
we have
[tex]b1=8\ cm[/tex]
[tex]b2=(4+8+2)=14\ cm[/tex]
[tex]h=4\ cm[/tex]
substitute the values
[tex]A=\frac{1}{2}[8+14](4)=44\ cm^{2}[/tex]
Answer:
D. 44cm^2
Step-by-step explanation:
A circle has a radius of 5ft and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measures of the central angle q?
Answers
Answer:
[tex]\frac{q}{360}[/tex] × π10 = 7
Explanation:
The formula to find arc length is [tex]\frac{x}{360}[/tex] × [tex]\pi r^{2}[/tex]
Simply plug in radius and arc length to get your equation.
Answer:
Central angle = 80.21°
Step-by-step explanation:
The arc length in circle is the product of radius and central angle made by the arc in radians.
That is
l = rθ
Here given the values r = 5 ft and l = 7 ft
Substituting
7 = 5 x θ
θ = 1.4 radians
[tex]\theta =1.4\times \frac{180}{\pi }=80.21^0[/tex]
Central angle = 80.21°
Please answer right away
Answers
Answer:
$29000 with a margin of error of $5000
Step-by-step explanation:
We have that the midpoint between the given values is
(X1+X2) / 2 = ($34000+$24000)/2 = $29000
We have that the midpoint between the given values would be
(X2-X1)/2=($34000-$24000)/2=$10000/2=$5000
So I can write that approach as $29000 with a margin of error of $5000
Done
What is the midpoint between (-2, -3) and (1, 0.5)
Answers
Answer:
(-1/2,-1.25)
Step-by-step explanation:
Once you plot the points, you should be able to find the midpoint formula.
The midpoint between the points (-2, -3) and (1, 0.5) is (-0.5, -1.25).
To find the midpoint between two points, you average the x-values and the y-values of the given points separately. The formula for the midpoint M between two points P1(x1, y1) and P2(x2, y2) is
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Applying this to the given points (-2, -3) and (1, 0.5), we calculate the midpoint as follows:
Average the x-values:
(-2 + 1) / 2 = -0.5
Average the y-values:
(-3 + 0.5) / 2 = -1.25
Find area of a cone
Show work
Answers
Answer: 138.16 in²
Step-by-step explanation:
You need to use this formula to calculate the surface area of the cone:
[tex]SA = \pi r^2 + \pi rl[/tex]
Where "r" is the radius, "h" is the height and "l" is the slant height.
To find the height you need to use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.
In this case:
[tex]a=l=7in\\\\b=r=\frac{8in}{2}=4in\\\\c=h[/tex]
("r" is the radius and "h" is the height and "l" is the slant height.)
You need to find "h". Then, solving for "h", you get:
[tex]h=\sqrt{(7in)^2-(4in)^2}\\h=5.74in[/tex]
Then, substituting values into the formula, you get:
[tex]SA = (3.14)(4in)^2 + (3.14) (4in)(7in)=138.16in^2[/tex]
The Roosevelts and the Jaspers live in the same city and pay the same sales
tax rate, and both families made $16,000 in taxable purchases last year, if the
Roosevelts made $91.000 and the Jaspers made 37000 last year, is the
sales tax in their city an example of a regressive tax?
Answers
Answer:
Yes, because the Jaspers paid a higher percentage of their income in sales tax than the Roosevelts did.
Step-by-step explanation:
Regressive tax is a constant, instead of a percentage of income. Those with a lower income would pay a higher percentage of their income. Both families, irregardless of income, paid $16,000 in taxes.
APEX
Answer:
Yes, because the Jaspers paid a higher percentage of their income in sales tax than the Roosevelts did.
Step-by-step explanation:
A regressive tax is one that collects a smaller percentage of the income as the person earns more. That is to say that at higher profit or higher income, the percentage of taxes that must be paid on the total tax base is lower.
In this way the poor are relatively more affected than the rich.
The Roosevelts made $91.000 (high income)
The Jaspers made $37.000 (low income)
But both paid the same sales tax rate of $16,000.
This type of tax does not have a redistribution effect of wealth. On the contrary, if it is a very high tax, it can accentuate inequality in a society.
Sal wants to build a robot. He puts a sphere on top of a cylinder.what will probably happen?
Answers
Answer:
It depends on which side of the cylinder. If she puts it on the curved side, it will roll off. If she puts it on the flat side and stabalizes it, it will stay in place if no further force is acted on it.
a fish tank is shaped like a rectangular prism. It has a length of 5 feet, a width of 2 feet, and a height of 3 feet. what is the volume of the fish tank?
Answers
Answer:
30 ft
Step-by-step explanation:
It is 30 because to find the volume of a rectangular prism, you do
length x width x height.
So, 5 x 2 x 3 = 30.
To find the volume of a rectangular prism, multiply its length, width, and height. Thus, the volume of the fish tank measuring 5 feet in length, 2 feet in width, and 3 feet in height is 30 cubic feet.
Explanation:The volume of a rectangular prism such as a fish tank can be calculated by multiplying its length, width, and height together. For a fish tank with a length of 5 feet, a width of 2 feet, and a height of 3 feet, the volume calculation would look like this:
Volume = Length × Width × Height
Volume = 5 ft × 2 ft × 3 ft
Volume = 10 ft × 3 ft
Volume = 30 ft³
Therefore, the volume of the fish tank is 30 cubic feet.
what is the midpoint of (-7,5)(7,3)
Answers
Answer:
(1,4)
Step-by-step explanation:
Answer:
The correct answer is (0,4)
Step-by-step explanation:
Ed decides to include more fruit in his diet he go to the grocery store over the weekend and buy six apples six oranges and six avocados the total cost is $19.50 write an equation
Answers
A=apple o=orange a=avocado
6A+6o+6a=19.50
Happy To Help! :D
Answer:
x + y + z = 3.25
Step-by-step explanation:
We are given that Ed buys six apples, six oranges and six avocados and their total cost is $19.50.
We are to write an equation representing this.
Assuming apples to be x, oranges to be y and avocados to be z, we can write it as:
[tex] 6 x + 6 y + 6 z = 1 9 . 5 0 [/tex]
Simplifying it by taking the common out to get:
[tex]x+y+z=3.25[/tex]
will mark brainliest!!
Solve the system of equations. x2 = y + x + 8
y = -x + 2
A) ( radical 10 , 2 - radical 10 ) and ( radical 10 , 2 + radical 10 )
B) ( radical 10 , 2 - radical 10 ) and (- radical 10 , 2 - radical 10 )
C) ( radical 10 , 2 - radical 10 ) and (- radical 10 , 2 + radical 10 )
D) ( radical 10 , -2 - radical 10 ) and (- radical 10 , 2 + radical 10 )
Answers
Answer:
the answer is A) ( radical 10 , 2 - radical 10 ) and ( radical 10 , 2 + radical 10 )
Step-by-step explanation:
what is the range of the function on the graph
Answers
Answer:
All real numbers greater than or equal to -2.
Step-by-step explanation:
The range is the set of values of the y-coordinates of the points on the graph.
The smallest y-coordinate is -2. All real numbers greater than equal to -2 are the range.
Answer: All real numbers greater than or equal to -2.
solve for X
x + 53 = 231
Answers
Answer:
x=178
Step-by-step explanation:
Since 53 is being added to x, you will subtract 53 from both sides. 231-53 equals 178, therefore x=178
Jon drove 365 on 20 gallons of gas. How many miles did he get per gallon?
Answers
Answer:
18.25
Step-by-step explanation:
365 ÷ 20 = 18.25
Jon drove 365 miles on 20 gallons of gas, so to find out how many miles he got per gallon, you divide 365 miles by 20 gallons. The result is 18.25 miles per gallon.
Explanation:To solve this problem, you need to divide the total number of miles that Jon drove by the number of gallons of gas he used. This is because the miles per gallon is calculated by dividing the total miles driven by the amount of gas used.
So, in this case, you would do the following calculation: 365 miles ÷ 20 gallons = 18.25 miles per gallon
This means that Jon got 18.25 miles per gallon of gas.
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Write and solve a quadratic equation for the situation below. Choose the answer that has both an equation that correctly models the situation as well as the correct solution for the situation. An isosceles right triangle has sides that are x + 2 units long and a hypotenuse that is 8 units long. What is the length of the missing sides of the triangle?
Answers
Answer:
2(x^2 + 4x - 28) = 0.
The length of the missing sides are:
4√2 units.
or 5.66 units ( to the nearest hundredth).
Step-by-step explanation:
Applying the Pythagoras Theorem:
8^2 = (x + 2)^2 + (x + 2)^2
2(x^2 + 4x + 4) = 64
2x^2 + 8x + 8 - 64 = 0
2x^2 + 8x - 56 = 0
2(x^2 + 4x - 28) = 0 models the situation.
Solving:
x = [- 4 +/- √(4^2-4*1*-28)] / 2
= (-4 +/- √128) / 2
= (-4 + 8√2) / 2 , (-4 - 8√2) / 2 (we ignore this negative root).
= -2 + 4√2.
This is 3.66 to the nearest hundredth.
So the length of the 2 equal sides is 2 + (- 2 + 4√2) = 4√2.
or 5.66 to the nearest hundredth.
A dilation produces a smaller figure. Which is a possible scale factor?
Answers
A dilation producing a smaller figure requires a scale factor less than 1. If the scale factor is 1/2, the model size is half the actual size. By setting up and solving a proportion, actual dimensions can be calculated.
Explanation:When a dilation results in a smaller figure, the scale factor used is less than 1. Think of the scale factor as a fraction where the actual size is the denominator and the model size is the numerator. For instance, a scale factor of 1/2 would mean that the model is half the size of the actual figure.
For a practical example: if we have a scale factor of 1:4 and the scale measurement is 4, the actual dimension can be found by setting up a proportion as 1/4=4/x, solving for x would give us the actual dimension, which in this case would be 16.
A rectangular block measures 3 cm x 4 cm x 3 cm how much water would it displace?
Answers
Answer:
36c^3m^3x^2
Step-by-step explanation:
you first multiply 3 cm by 4 cm by 3 cm to get 36 cm.its mass in air and its effective mass when submerged in water (density = 1 gram per cubic centimeter).1.0 g/cm3then you get the answer 36c^3m^3x^2Which of the following statements shows a characteristic of a statistical question?
Answers
Answer:
For a question to be statistical it has to have a specific population, room for a clear response, and a variability in the data.
An example of a statistical question is, "What is the typical amount of time it takes for a piece of gum to lose its flavor?" This is statistical because it accounts for a clear response, population, and variability.
Answer:
The question asks for a quantitative response.
Step-by-step explanation:
I did the 8.01 test, C was the correct answer.
Good luck FLVS students
36+4x=x^2+15
What is x?
Answers
X = -3 or X = 7
Step 1: Simplify both sides of the equation.
Step 2: Subtract x^2+15 from both sides.
Step 3: Factor left side of equation.
Step 4: Set factors equal to 0.
Answer:
x=7 or x=-3
Step-by-step explanation:
36+4x=x^2+15
36-15+4x=x^2
21+4x=x^2
0=x^2-4x-21
0=x^2-(7-3)x-21
0= x^2-7x+3x-21
0= x(x-7)+3(x-7)
0= (x-7)(x+3)
so either
x-7=0
x=7
or x+3=0
x=-3
Please answer.
The table represents the function f(x) = 2x+1
Which value goes in the empty cell?
A)3
B)5
C)8
D)23
Answers
Replace the x in the equation with the x value in tha table for the missing f(x) and calculate:
f(x) = 2x +1 = 2(2) +1 = 4 +1 = 5
The answer is B) 5
The table represents the function f(x) = 2x +1. The value goes in the empty cell is 5. The answer is B) 5.
What is a function?A function is a type of relation, or rule, that maps one input to specific single output.
The table represents the function
f(x) = 2x +1
Replace the x in the equation with the x value in the table for the missing f(x)
F( 2) = 2(2) +1
F( 2) = 4 +1
F( 2) = 5
The answer is B) 5
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Which equation is graphed here?
Answers
Answer:
The third one or the first one
Step-by-step explanation:
Can't be +4 or -4
Answer:
The equation of the line on the graph is y - 4 = -3(x+1)
If a data set has 20 data values, the number of values in the upper quartile is ?
Answers
Answer:
the answer is 5.5
explanation:
just did the test
Answer: The uper quatile Q3=15.75
Step-by-step explanation:
Q3=3/4(N+1)
Q3=3/4(20+1)
Q3=3/4(21)
Q3=63/4
Q3=15.75