# MAT1275/D225 – Spring 2024

Instructor: Suman Ganguli

The college is closed for spring break Monday April 22 thru Tuesday April 30, so our next class will be Wednesday May 1.

I have reopened a number of WebWork sets, so you can use this time to complete any WebWork exercises from the following sets that you didn’t do earlier in the semester:

• Expressions-Arithmetic-Integer Exponents
• Expressions-Polynomials-Linear Expressions
• Expressions-Polynomials-Multiply Polynomials
• Expressions-Polynomials-Factor Trinomials
• Expressions-Polynomials-Factor Trinomials AC Method
• Expressions-Rational Expressions-Adding and Subtracting Part 1
• Expressions-Rational Expressions-Complex Fractions 1

I will also be opening some WebWork sets on trigonometry over te break so that you can get started on that topic, which we will discuss when we get back.

We will have only 3 weeks left in the semester after we come back from spring break–the final exam will be on Wednesday May 22.

We will also have a third midterm exam in the week before the final, which will cover trigonometry plus some topics from earlier in the semester (as review for the final).

## Announcements

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

Review for the exam by reviewing the listed WebWork exercises (complete the exercises on the open WebWork sets below). You can also review the related examples we have done in class and on the quizzes–including the examples we did in class today.

WebWork:

• Quadratic Equations-Zero Product – due Mon April 15 (Sec 2.2.1)
• Quadratic Equations-Completing the Square – due Wed April 17 (Sec 2.2.3)
• Graphs-Graphs of Quadratic Equations – due date TBA (after spring break — but please do at least #7-9, which are good review for the exam)

## Topics

We did a few examples of 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 reviewed how we find these points on the graph:

An example from the WebWork of finding the vertex of a given quadratic by completing the square to put it in vertex form. We also found the x- and y-interecepts, and sketched a graph:

Another example from the WebWork, but here we find the vertex using the vertex formula:

We closed with an exercise from the Final Exam Review shooet (#2(b)). We again use the vertex formula to find the vertex; in this example, we use the zero product property to solve the quadratic equation and thus find the x-intercepts, since the quadratic factors:

Besides the material on quadratic equations, please also review complex fractions and multiplication/division of complex numbers for the exam:

## Announcements

WebWork:

• Quadratic Equations-Zero Product – due Mon April 15 (Sec 2.2.1)
• 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:

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