SAT Math Multiple Choice Question 292: Answer and Explanation
Vadim graphs the equation y = –3x2 + 8, which is shown in the figure above. He realizes, however, that he miscalculated and should have graphed How will this affect his graph?
- A. It will change the y-intercept.
- B. It will make the parabola open in the opposite direction.
- C. It will make the parabola cross the x-axis closer to the origin.
- D. It will make the parabola cross the x-axis farther from the origin.
Correct Answer: D
Category: Passport to Advanced Math / Quadratics
Strategic Advice: Don't waste time trying to graph the second equation. Instead, think about the question conceptually. The magnitude of the coefficient of x2 (not the sign) determines how wide or narrow the graph is.
Getting to the Answer: Changing the coefficient of x2 from -3 to will make the graph narrower or wider (in this case, wider), which means the only things that will change are the x-intercepts. This means you can eliminate A and B. To choose between C and (D), recall that fraction coefficients (between 0 and 1) result in wider graphs, so the x-intercepts will spread out and therefore be farther from the origin.