Month: September 2018

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.

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.