Question

Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.

f(x)=2(x−8) ^2−3

Answer 1

It's a minimum, at (8, -3)

Explanation:

Option 1: you unwrap the square , add like terms, and then recognize it's a parabola and find the coordinates of the vertex.

Or look at it as -3 + something ^2. It means you are adding something positive to -3, so the sum is greater or equal to -3, that is the definition of a minimum. At that point you find the minimum by setting that something equal to 0 (which gives you x = 8) and the value is -3 + 0 = -3