# How do you write the vertex form equation of the parabola y=x^2-16x+71?

Dec 29, 2017

$y = {\left(x - 8\right)}^{2} + 7$

#### Explanation:

The $x$-coordinate of the vertex, which is often called $h$, can be found by computing $h = - \frac{b}{2 a}$.

For this problem: $h = - \frac{- 16}{2 \left(1\right)} = 8$.

To find the $y$-coordinate of the vertex, often called $k$, we substitute $h$ in for all the $x$s we see in the original:

$k = {\left(8\right)}^{2} - 16 \left(8\right) + 71 = 64 - 128 + 71 = 7$.

The vertex is $\left(h , k\right)$, so for this problem $\left(8 , 7\right)$.

Vertex form of the equation is: $y = a \cdot {\left(x - h\right)}^{2} + k$. We've found $h$ and $k$. The value of $a$ is the coefficient of ${x}^{2}$ in the original, so $a = 1$.

The equation we're looking for is: $y = {\left(x - 8\right)}^{2} + 7$.