Question

For the function y=-2x^2+4x+1, what are the coordinates of the vertex? Is it a maximum or minimum point? Hint: use the vertex/axis of symmetry formula for x. Show all work algebraically to earn full credit and use Desmos only to check your answer

Answer 1

Step-by-step explanation:

y = -2x² + 4x + 1

Complete the square.

y = -2 (x² − 2x) + 1

y = -2 (x² − 2x + 1) + 1 − (-2)(1)

y = -2 (x − 1)² + 3

The vertex is (1, 3).  The leading coefficient is negative, so the vertex is a maximum.

Graph: desmos.com/calculator/qsih3rd8ev