Question

How do you find the maximum and minimum of `y=2(x+2)^2-4/5`?

Answer 1

Vertex`->(x,y)=(-2,-4/5)` and is a minimum

Explanation:

This is a quadratic equation but in vertex form (completing the square). They use this form as you may almost read the coordinates directly off it.

If you were to multiply out the brackets the `x^2` term would be `+2x^2`

As this is positive the graph is of form `uu` Thus there is a minimum

Given that: `" "y=2(x+color(magenta)(2))^2color(blue)(-4/5)`

Then

`x_("vertex")=(-1xxcolor(magenta)(2))=-2`

`y_("vertex")=color(blue)(-4/5)`

Vertex`->(x,y)=(-2,-4/5)`