# Question #0be35

May 4, 2017

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

#### Explanation:

We have the vertex $\left(5 , 2\right)$, 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: $\textcolor{b l u e}{y = a \left(x - h\right) + k}$
$y = a {\left(x - 5\right)}^{2} + 2$

Expand:
$y = a \left({x}^{2} - 10 x + 25\right) + 2$

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

$y = - \left({x}^{2} - 10 x + 25\right) + 2$

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

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