# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function f(x) = x^2 + 6x - 7?

Nov 2, 2017

Vertex $\left(- 3 , - 16\right)$

Axis of symmetry $x = - 3$

#### Explanation:

Given -

$y = {x}^{2} + 6 x - 7$

Vertex

$x = \frac{- b}{2 a} = \frac{- 6}{2 \times 1} = - 3$

At $x = - 3$

$y = {\left(- 3\right)}^{2} + 6 \left(- 3\right) - 7$
$y = 9 - 18 - 7 = - 16$

Vertex $\left(- 3 , - 16\right)$

Axis of symmetry $x = - 3$

Since the coefficient of ${x}^{2}$ is positive, the parabola opens up.

Take a few points on either side of $x = - 3$. Find the corresponding $y$ values . plot them on a graph sheet. join all the points with the help of a smooth curve. You get the parabola.