Y=-2x^2+12x-16 is my quadratic equation.

Question

Can you please show me how to find the maximum and minimum of this equation.

Answer 1

Sure!

Since this is "Algebra 2", I assume you do not have calculus yet.

The general quadratic equation is Ax² + Bx + C = y

The vertex [which is where the maximum (or minimum) occurs} occurs at x = -B/2A

In this case the maximum occurs when x = 3 (-12/(2*-2).

Now you ask, legitimately, how do I know this? The easiest answer comes from calculus, but if you graph

quadratic equations, you will convince yourself that this is correct. You can also convince yourself by calculating the value of y when x is near -B/2A but not equal to it.