5

Set 16: Quadratic Equations

Explanation

Answer: A

Find the x-intercepts of y=(x3)(x+2)y = (x - 3)(x + 2).

A.

(3,0)(3, 0) and (2,0)(-2, 0)

✓ Correct
B.

(3,0)(-3, 0) and (2,0)(2, 0)

C.

(0,3)(0, 3) and (0,2)(0, -2)

D.

(3,2)(3, -2)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. The x-intercepts are found by setting y=0y = 0. 1. Set (x3)(x+2)=0(x - 3)(x + 2) = 0. 2. Apply Zero Product Property: * x3=0x=3x - 3 = 0 \Rightarrow x = 3 * x+2=0x=2x + 2 = 0 \Rightarrow x = -2 3. The coordinates are (3,0)(3, 0) and (2,0)(-2, 0). Choice B is incorrect because of sign errors (common mistake). Choice C is incorrect because it lists them as y-intercepts. Choice D is incorrect because it combines them into one point.

Key Steps:

The correct answer is (3,0)(3, 0) and (2,0)(-2, 0)

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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