Month: April 2024 (Page 2 of 3)

Announcements

WebWork:

• Quadratic Equations-Completing the Square – due Fri April 10 (Sec 2.2.3)
• Quadratic Equations-Zero Product – due Wed April 10 (Sec 2.2.1)
• Quadratic Equations-Quadratic Formula – due Mon April 15
• Graphs-Graphs of Quadratic Equations – due Wed April 17

Topics

We reviewed again our techniques for solving quadratic equations:

We then focused on applying the quadratic formula, with examples from the WebWork:

Another example from the Webwork–note that because the “discriminant” b^2 – 4ac < 0, we have “no real solutions” and instead have 2 complex solutions (but this WebWork exercises requires that you enter the solutions in terms of the square root of the negative number):

We then shifted to talking about graphs, in particular of “y = a linear expression” (straight lines) and “y = a quadratic expressions” (parabolas):

Review of equations and graphs of lines:

For quadratics, we started with the simplest such, y = x^2:

We discussed how the “roots” of a quadratic polynomial (the solutions of “ax^2 + bx + c = 0”) give the x-coordinates of the x-intercepts of the graph y = ax^2 + bx + c:

Announcements

WebWork:

• Quadratic Equations-Completing the Square – due Wed April 10 (Sec 2.2.3)
• Quadratic Equations-Zero Product – due Wed April 10 (Sec 2.2.1)
• Quadratic Equations-Quadratic Formula – due Mon April 15
• Graphs-Graphs of Quadratic Equations – due Wed April 17

Topics

We are now focusing on quadratic equations. We started by reviewing what we have discussed previously–“expressions”–and now equations:

We outlined the various techniques we have for studied for solving quadratic equations:

We reviewed applying the square root property, for solving quadratic equations in a certain form:

And we went through an example of solving a quadratic equation by completing the square–in this case we can also solve this equation by factoring and using the zero product property:

Recall that we used completing the square, together with the square root property, to derive the quadratic formula. We will also use the technique of completing the square for analyzing graphs of quadratic expressions, and for graphs of circles.