# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function p(x)=(x+5)^2-3?

May 13, 2018

As it is a positive ${x}^{2}$ it is a $\cup$ shaped parabola so it is a minimum. The minimum point is (-5,-3) and the line of symmetry is $x = - 5$

$y = {\left(x + 5\right)}^{2} - 3$

$y = {x}^{2} + 10 x + 25 - 3$

$y = {x}^{2} + 10 x + 22 \implies \left(0 , 22\right)$ is the y intercept

Put the values x =-4, -3, -2 and -1 into the equation to give

y=-2, 1, 6, and 13

Plot these points and then copy them on the left of the line of symmetry.