Question

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`?

Answer 1

As it is a positive `x^2` it is a `uu` shaped parabola so it is a minimum. The minimum point is (-5,-3) and the line of symmetry is `x=-5`

`y=(x +5)^2-3`

`y=x^2+10x+25-3`

`y=x^2+10x+22 => (0,22)` 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.