Question

Question #0be35

Answer 1

`y=-x^2+10x-23`

Your answer is correct, I'm not sure why that website says the answer is wrong...

Explanation:

We have the vertex `(5,2)`, and the parabola has a negative `a` value because the graph is convex.

Looking at the other point (4,1), we can tell that the `a` value is equal to `-1` because of the slope, but just to confirm:

Vertex form: `color(blue)(y=a(x-h)+k)`
`y=a(x-5)^2+2`

Expand:
`y=a(x^2-10x+25)+2`

Try the point `(4,1)` to determine the value of `a`
`1=a(16-40+25)+2`
`1=a+2`
`a=-1`

`y=-(x^2-10x+25)+2`

`y=-x^2+10x-25+2`

`y=-x^2+10x-23`