Question

Jessica is asked to write a quadratic equation to represent a function that goes through the point (8, –11) and has a vertex at (6, –3). Her work is shown below.

–11 = a(8 – 6)2 – 3
–11 = a(2)2 – 3
–11 = 4a – 3
–8 = 4a
a = –2

After Jessica gets stuck, she asks Sally to help her finish the problem. Sally states that Jessica needs to write the quadratic equation using the value she found for a, –2, and the point (8, –11).

Evaluate Jessica’s work and Sally’s review to determine which statement is true.

Answer 1

Jessica solved for the correct value of a, but Sally's review was incorrect. 

Answer 2

Jessica’s work is correct and Sally’s review is incorrect

Explanation:

I'm just assume it's a vertical parabola

we know that

The equation of a vertical parabola in vertex for is equal to

`y=a(x-h)^(2)+k`

where

(h,k) is the vertex

In this problem we have

`(h,k)=(6,-3)`

point
`(8,-11)`

substitute

`-11=a(8-6)^(2)-3`

`-11=a(2)^(2)-3`

`-11=4a-3`

`-8=4a`

`a=-2`

To find the equation using the value of a and the vertex point

so

`y=-2(x-6)^(2)-3`

therefore

Jessica’s work is correct and Sally’s review is incorrect