SAT Math Multiple Choice Question 424: Answer and Explanation
4. If a = 0 and b < 0, then which of the following could be the graph of f(x) = (x – a)(x – b)?
Correct Answer: A
Category: Passport to Advanced Math / Quadratics
Strategic Advice: If a = 0, then one factor must be (a – 0), which means x = 0 is a root. This means the graph must cross through the origin, so you can eliminate C and D right away.
Getting to the Answer: Look at the remaining two choices, (A) and B. The question states that b < 0. This means b is negative, which means the other x-intercept must fall to the left of the y-axis, so (A) is correct.
Because this question is in the calculator section of the test, you could also use the Picking Numbers strategy. Choose a value for b (that is less than 0), such as –2, and graph the equation y = (x – 0)(x – (–2)) to see what the graph looks like.