Question

the graph below is a translated reflection of the graph of the parent function. Write the quadratic function to model the graph.​

Answer 1

Answer:   $y=-\dfrac{16}{9}(x+3)^2+4$

Step-by-step explanation:

Use the vertex formula:  y = a(x - h)² + k    where

• a is the vertical stretch
• -a is a reflection over the x-axis
• (h, k) is the vertex

We can see that the vertex of the curve is (-3, 4)  -->  h = -3, k = 4

and it is a reflection over the x-axis --> a-value is negative

We need to find the a-value. Choose another point on the curve and plug it into the vertex formula for (x, y) and then solve for a.

I will choose (x, y) = (-3/2, 0)

$0=a\bigg(\dfrac{-3}{2}+3\bigg)^2+4\\\\\\-4=a\bigg(\dfrac{3}{2}\bigg)^2\\\\\\-4\bigg(\dfrac{2}{3}\bigg)^2=a\\\\\\-\dfrac{16}{9}=a$

Now that we know the vertex and the a-value, we can input them into the vertex formula:

                         $\large\boxed{y=-\dfrac{16}{9}(x+3)^2+4}$

Answer 2

Answer:

Answer:  

Step-by-step explanation:

Use the vertex formula:  y = a(x - h)² + k    where

a is the vertical stretch

-a is a reflection over the x-axis

(h, k) is the vertex

We can see that the vertex of the curve is (-3, 4)  -->  h = -3, k = 4

and it is a reflection over the x-axis --> a-value is negative

We need to find the a-value. Choose another point on the curve and plug it into the vertex formula for (x, y) and then solve for a.

I will choose (x, y) = (-3/2, 0)

Now that we know the vertex and the a-value, we can input them into the vertex formula: