# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y = x^2 - 2x - 10?

Jul 8, 2017

Complete the square

#### Explanation:

In this case, completing the square would give you:

$y = {\left(x - 1\right)}^{2} - 11$

Once in this form $y = {\left(x - p\right)}^{2} + q$, the negative of p is the x coordinate of the vertex of the graph and q is the y coordinate. This means the minimum (as the coefficient of ${x}^{2}$ is positive (1)) of the graph will be at ( 1 , -11 ) and the line of symmetry will pass through the x coordinate, namely $x = 1$

Jul 8, 2017

Axis of symmetry: $x = 1$; minimum value $- 11$

#### Explanation:

graph{x^2-2x-10 [-28.52, 29.22, -14.43, 14.45]}

A quadratic equation in standard form is $y = a {x}^{2} + b x + c$. In this case, $a = 1$, $b = - 2$, and $c = - 10$.
To find the axis of symmetry, use the formula $x = - \frac{b}{2 a}$.

$x = - \frac{b}{2 a}$
$x = - \frac{- 2}{2 \left(1\right)}$
$x = 1$

The graph above shows that the parabola is an upward-facing one, so it has a minimum value. The max or min is always on the axis of symmetry, so you can substitute $x = 1$ into the function.

$y = {x}^{2} - 2 x - 10$
$y = {1}^{2} - 2 \left(1\right) - 10$
$y = - 11$

So, the axis of symmetry is $x = 1$ and the minimum value is $- 11$. You can also write the minimum as the coordinate $\left(1 , - 11\right)$.