Multiple choice

g(x) = -3(x + 2)2 + 27 The quadratic function g is defined as shown. In the xy-plane, the graph of y = g(x) intersects the x-axis at the points (p, 0) and (q, 0), where p and q are constants. If q > 0, what is the value of q?

  1. 1

  2. 3

  3. 4

  4. 5
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A Correct answer
Explanation

To find the x-intercepts, set g(x) = 0: -3(x + 2)^2 + 27 = 0. This simplifies to (x + 2)^2 = 9, so x + 2 = 3 or x + 2 = -3. Thus, x = 1 or x = -5. Since q > 0, q must be 1.

AI explanation

To find the x-intercepts, set g(x) = 0 to get -3(x + 2)^2 + 27 = 0. Isolating the squared term gives (x + 2)^2 = 9, and taking the square root of both sides results in x + 2 = 3 or x + 2 = -3. Solving these two equations yields x = 1 and x = -5; since q > 0, q must be 1.

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