Question

One quadratic function has the formula h(x) = -x 2 + 4x - 2. Another quadratic function, g(x), has the graph shown below

Which option below best describes the maximums of these two functions?

Functions g and h have the same maximum of -2.
Functions g and h have the same maximum of 2.
Function h has the greater maximum of -2.
Function g has the greater maximum of 2.

Answer 1

Functions g and h have the same maximum of 2.

Explanation:

Answer 2

We are comparing maxima. From the graph we know that the max of one graph is +2 at x = -2. What about the other graph? Need to find the vertex to find the max.

Complete the square of h(x) = -x^2 + 4x - 2:

h(x) = -x^2 + 4x - 2 = -(x^2 - 4x) -2
= -(x^2 - 4x + 4 - 4) - 2
=-(x^2 - 4x + 4) -2+4
= -(x-2)^2 + 2 The equation describing this parabola is y=-(x-2)^2 + 2, from which we know that the maximum value is 2, reached when x = 2.

The 2 graphs have the same max, one at x = -2 and one at x = + 2.