Which of the following numbers are in set A? Check all that apply.

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

The equation of a vertical parabola written in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

$f(x)=a(x-2)^2-8$

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

$0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2$

therefore

The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

$f(x)=a(x-x_1)(x-x_2)$

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

so

$f(x)=a(x-0)(x-4)$

$f(x)=ax(x-4)$

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

$-8=a(2)(2-4)\\-8=-4a\\a=2$

therefore

The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

4 0

3 years ago

What is the answer to this problem

Aleks04 [339]

Answer:

14 cm^2

Step-by-step explanation:

You find the area of both triangles, and subtract by 4

6x3x1/2x2 - 2x2

18 - 4

14

3 0

2 years ago

4. Benson sells vacuum cleaners on a commission. He earns $75 for each vacuum cleaner he sells.

Wittaler [7]

He would have to sell at least 19 vacuums.

8 0

3 years ago

Read 2 more answers

Which of the following is the most appropriate unit.to describe the rate at which a person reads

BaLLatris [955]

The answer is a words per minute, because the independent quantity is the words

8 0

3 years ago

Translate (3, – 4) down 3 units.<br> Then reflect the result over the y-axis.

Greeley [361]

Answer:

Step-by-step explanation:

Best advice: make a sketch (which I can't do here).

When you reflect in the x axis, only the y value changes...so (3, -4) reflects to (3,4).

Translating down (i.e. in the negative direction) again means the x value (the abscissa) doesn't change, only the y value (the ordinate)...so the final value of the point is (3,1).

3 0

2 years ago