Announcements

WebWork:

  • Quadratic Equations-Zero Product – due Mon April 15 (Sec 2.2.1)
  • Quadratic Equations-Quadratic Formula – due Mon April 15
  • Quadratic Equations-Completing the Square – due Mon April 17 (Sec 2.2.3)
  • Graphs-Graphs of Quadratic Equations – due date TBA

Our 2nd midterm exam will be on Wednesday April 17. Please see this OpenLab post with a list of topics and review exercises: Exam #2 Review Topics.

Please start reviewing for the exam by reviewing the listed WebWork exercises (complete the exercises on the open WebWork sets above). You can also review the related examples we have done in class and on the quizzes.

Topics

We discussed graphs of quadratics–“parabolas.” The key points on such graphs that we want to identify are the y-intercept, the x-intercept(s), and the vertex:

We then discussed “vertical” and “horizontal” shifts of y = x^2, and how there are represented algebraically:

Combining vertical and horizontal shifts, we arrive at the “vertex” form of a quadratic polynomial:

y = (x – h)^2 + k

for which the vertex is the point (h, k):

Given y = x^2 + bx + c, we can put it in vertex form by completing the square:

An example showing how we find the y-intercept, the x-intercepts (in this case we solve the quadratic equation by factoring), and the vertex, by completing the square: