Question

Maximum and Minimum Values of General Quadratic Functions

1. By expressing y = 2x^2 + 4x + 17 in the form y = a(x + b)^2 + C, where a, b, and c are constants, state the minimum value of y and the value of x at which this occurs. Hence, sketch the curve y = 2x^2 + 4x + 17
x =
y =​

Answer 1

x=-1

y=15

Explanation:

This works because completing the square is essentially demonstrating what g(x) - where g(x) in this case = x^2 - would have to be translated by to give the function you have.

So by completing the square you have shown that the function you've been given has been shifted to the left by -1, stretched by a factor of 2 along the y axis and shifted up by 15.