Category: 11 SL Homework

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11 SL Domain and Range

Read section 2C and complete the questions below before our next class.

Exercise 2C questions 1–3, 4aceik

We didn’t quite get to this material in class today, but if you do want to work ahead you can read section 2D, and complete the questions below as well.

Exercise 2D questions 3, 5–7

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11 SL Applications and Optimization of Quadratics

Complete the questions below before our next class on Monday. (These questions will also help you to prepare for the test on Thursday next week.)

Exercise 1F questions 1–5, 7, 9, 12, 15
Exercise 1G questions 2, 3, 7

On Monday we’ll discuss

  • the solutions to these questions, as well as
  • any difficulties you may have had with the review questions that were suggested here.
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11 SL Quadratics: Intersecting Quadratics

Complete the following questions before our next class (tomorrow).

Exercise 1E questions 1abd, 2, 3

A harder question that you might also try is question 4. If you do try this question tonight, you’ll probably find that Example 24 in the textbook is helpful.

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11 SL Polynomials Challenge

The questions below are optional, but if you can answer them correctly, please do show your solutions to Dr. McDonald! (Also, the equations won’t show up correctly in an email, so click to see these questions on the website if you’ve received an email notice for this post.)

Consider the quadratic equation \(ax^2+bx+c=0\), with \(a\neq 0\) for questions 1 and 2.

  1. Complete the square to find another expression for the left side of the equation.
  2. Use your answer from question 1 to isolate \(x\). What is the name of the formula you’ve just derived?
  3. Consider the quadratic function \(f(x)=3x^2+kx-4\), where \(k\) is some constant real number. Explain how you know that, no matter the value of \(k\), the graph of \(f\) will always have two \(x\)-intercepts.
  4. Consider the quadratic function \(f(x)=x^2+kx-(k+8)\), where \(k\) is some constant real number. For which value of \(k\) will the \(x\)-intercepts of the graph of \(f\) be closest together?
  5. Are there any quadratic functions that can’t be represented in factored form? Are there any quadratic functions that can’t be represented in vertex form? Explain your answers.
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11 SL The Discriminant

Since we didn’t quite finish the material in our last class, the questions below are (part of) the question set you should complete by Thursday (our second class this week).

If you want to get a head start on your homework now, have a look at the questions below.

Exercise 1A.3 questions 1abc, 2abde
Exercise 1B questions 1, 2abc, 3ab, 4abcf