Question #0be35

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Answer 1 · 2017-05-04T21:27:42

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

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

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 $a$
$1=a(16-40+25)+2$
$1=a+2$
$a=-1$

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

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

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