# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y = x^2 + 4x - 5 ?

May 10, 2017

${y}_{\min} = - 9$

Axis of symmetry $x = - 2$

#### Explanation:

we first of all need to complete the square before we find the required information.

$y = {x}^{2} + 4 x - 5$

$y = \left({x}^{2} + 4 x\right) - 5$

half the coefficient of x , square it; then add and subtract it

y=(x^2+4x+color(blue)(2^2))-5-color(blue)(2^2

The bracket is now a perfect square

$y = {\left(x + 2\right)}^{2} - 9$

because the graph is $+ {x}^{2}$ we will have a minimum.

This minimum occurs at the vertex
ie when $\left(x + 2\right) = 0$

so minimum occurs at $x = - 2 \implies {y}_{\min} = - 9$

The axis of symmetry is the line through the vertex

ie.$\text{ } x = - 2$

graph{x^2+4x-5[-7,5,-12,5]}

(The scale of the graph is set to show intersection points - it won't look like this on graph paper!!!)