SAT Math Multiple Choice Question 612: Answer and Explanation

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Question: 612

12. What is the total number of x- and y-intercepts in the graph of the equation y = (x + 2)2(x - 3)2?

  • A. Two
  • B. Three
  • C. Four
  • D. Five

Correct Answer: B

Explanation:

B Advanced Mathematics (polynomials) MEDIUM-HARD

Given equation:

y = (x + 2)2 (x - 3)2

To find the y-intercept, set x = 0:

y = (0 + 2)2(0 - 3)2

Simplify:

y = (2)2(-3)2 = (4)(9) = 36

Therefore the y-intercept is at (0, 36).

To find the x-intercepts, set y = 0:

0 = (x + 2)2 (x - 3)2

By the Zero Product Property, the only solutions to this equation are x = -2 and x = 3, so there are two x-intercepts and a total of three x- and y-intercepts.

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