Question

For the function = − + + , what are the coordinates of the vertex? Is it a maximum or minimum point? Show all work algebraically to earn full credit.

Answer 1

Answer:

Vertex: (1,3)

Maximum

Step-by-step explanation:

Given the quadratic function $y=-2x^2+4x+1$.

First, find the coordinaes of the vertex:

$x_v=\dfrac{-b}{2a}=\dfrac{-4}{2\cdot (-2)}=\dfrac{-4}{-4}=1\\ \\y_v=-2\cdot 1^2+4\cdot 1+1=-2+4+1=3$

Hence, the vertex is at point (1,3).

The leading coefficient is -2, this means parabola opens downwards and the value of the function at vertex is the maximum value of the function.