SAT Math Multiple Choice Question 926: Answer and Explanation
10. Etienne is graphing the quadratic equation y = x2 – 8x – 48. He substitutes 0 for x and finds that the y-intercept of the graph is –48. Next, he wants to plot the x-intercepts of the graph, so he rewrites the equation in a different form. Assuminghe rewrote the equation correctly and the equation reveals the x-intercepts, which of the following is Etienne's new equation?
Correct Answer: D
Category: Passport to Advanced Math / Quadratics
Strategic Advice: Quadratic equations can be written in several different forms, each of which reveals something special about the graph. For example, the vertex form of a quadratic equation (y = a(x - h)2 + k) gives the minimum or maximum value of the function (k), while the standard form (y = ax2 - + bx + c) reveals the y-intercept (c).
Getting to the Answer: The factored form of a quadratic equation reveals the solutions to the equation, which graphically represent the x-intercepts. You can eliminate A and B because the equations are not written in factored form. To choose between C and (D), you need to determine which is the correctly factored form of the given equation. The factors of -48 that add up to -8 are -12 and 4, so the factors are (x - 12) and (x + 4), which means (D) is correct.