Instructor: Suman Ganguli

# Month: April 2024(Page 2 of 3)

Our second midterm exam will be next Wednesday (Wed April 17). Please continue working on the open WebWork sets, especially the exercises listed below; you should also review the exercises listed below from earlier WebWork sets. The best preparation for the exam is to write out solutions to the WebWork exercises listed below.

Also listed below are some exercises from the MAT1275 Final Review sheet, which is available as a pdf on the Math Department website here, and also on our OpenLab Files. You can also write out solutions to these Final Exam Review exercises to review for this exam (and to prepare for the final exam!)

You should also review your class notes and the Class Recaps here on OpenLab, since we did most of these WebWork examples in class–see Class Recaps #12-22.

You should also review the Quiz #3 and Quiz #4 solutions, which are available on OpenLab Files. You can also review relevant examples from the textbook.

(I will update the list below with specific textbook examples to review.)

Here are the topics and relevant exercises/examples to review:

Simplifying complex fractions:

Quiz #3

WebWork: “Rational Expression-Complex Fractions 2” #1-3

Final Exam Review: #3

Multiplication and division of complex numbers:

Quiz #4

WebWork: “Complex Numbers” #4-7

Final Exam Review: #5

via factoring and the zero product property:

WebWork: “Quadratic Equations – Zero Product”: #2-6

(review factoring of quadratic expressions from Exam #1 if necessary)

via completing the square and the square root property:

Quiz #4

WebWork”Quadratic Equations – Square Root”: #2-6

WebWork: “Quadratic Equations-Completing the Square”: #3-5

via the quadratic formula (including simplifying square roots):

Final Exam Review: #1

WebWork: “Graphs of Quadratic Equations”: #7-9

Final Exam Review: #2

## 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)
• 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)
• 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.

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