In the following​ exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function.

Question

f(x)=2(x-4)^2-2

The vertex is ____

​(Type an ordered​ pair.)

Answer 1

Hello, Gabriela,

We can either graph of find the first derivative of the function and set it to zero to find the vertex. Try graphing it - you'll find the vertex quickly. But it you look at what the equation is telling us, the portion"(x-4)" is boldly suggesting that we try x=4. That reduces the first part of the equation to 0. No matter what the exponent is, 0ⁿ will be zero, leaving just the "-2."

At x = 4, y = -2. No other value of x will get us below this point.

So the vertex is (4,-2).

Bob