Question

For the function y=-2x^2 + 4x +1, what are the coordinates of the vertex? Is it a maximum or minimum point? Consider using x = -b/2a. Show all work algebraically.

Vertex: _________ is this a Minimum or Maximum?

Answer 1

Answer:

The vertex is (1, 3). It's a max.

Step-by-step explanation:

I'm gonna use completing the square to solve for the vertex.

y = -2x² + 4x + 1     ,     dividing by -2

y = x² - 2x - 1/2

y = x² - 2x + 1 - 1 - 1/2

y = (x² - 2x + 1) +(- 1 - 1/2)

y = (x² - 1)² + (- 1.5)     ,     multiplying back in the -2 I divided earlier

y = -2(x² - 1)² + -2(- 1.5)

y = -2(x² - 1)² + 3

Equation is now in form of y = a(x² - h)² + k where the vertex is (h, k).

y = a(x² - h)² + k

y = -2(x² - 1)² + 3

So the vertex is (1, 3).

It's a max because y = -x². A negative x² will form a frowning face; the curve will point down forming a max point.