Michigan State University - Diagnostic Exam

4.1

  •   The x-coordinate of the maximum point on the graph of y= - x2 - 4x + 3  is

    a) -2 b) 2 c) -4 d) 4 e) 7

Solution:

The graph of y = - x2 - 4x + 3  is shown below. The maximum occurs at the vertex.

PIC


To find the coordinates we complete the square

y =  - (x2 + 4x ) + 3 = - (x2 + 4x + 4) + 3 - (- 4) = - (x + 2)2 + 7

It follows that the coordinates of the vertex are (- 2, 7)  .

Diagnostic:

If you miss this question please review finding the vertex of a quadratic function.

Also, see 3.11: Quadratic Functions .


July 15, 2008