How do you find the vertex of y = x^2 – 10x + 5?

May 28, 2017

The formula for x coordinate, h, of the vertex of a parabola described by an equation of the form $y = a {x}^{2} + b x + c$ is:
$h = - \frac{b}{2 a}$
The y coordinate, k, is found by evaluating the function at $x = h$.

Explanation:

Given: y = x^2 – 10x + 5

By observation, $a = 1 , b = - 10 \mathmr{and} c = 5$

The x coordinate of the vertex is:

$h = - \frac{- 10}{2 \left(1\right)}$

$h = 5$

Obtain the y coordinate, k, by evaluating the function at $x = 5$:

k = 5^2 – 10(5) + 5

$k = 25 - 50 + 5$

$k = - 20$

The vertex is the point $\left(5 , - 20\right)$.