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

Vertex: (1,3)

Maximum

Explanation:

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

First, find the coordinaes of the vertex:

`x_v=(-b)/(2a)=(-4)/(2\cdot (-2))=(-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.