Question

30 pointssss!!!!!!!!!

A quadratic function f(x) reaches a minimum value of -16 when x = 2 and the graph of f(x) passes through the x-axis at 6 and -2. Which of these are equivalent forms of the function f(x) ? Choose all that are correct.
A . f(x) = x ^ 2 - 4x - 12
B. f(x) = (x - 2) ^ 2 - 16
C. f(x) = (x - 2)(x + 16)
D. f(x) = (x - 6)(x - 2)
E. f(x) = (x - 6) ^ 2 + 2
F. f(x) = x ^ 2 - 8x + 12

Answer 1

A . f(x) = x ^ 2 - 4x - 12

B. f(x) = (x - 2) ^ 2 - 16

Explanation:

Don't pick C; it's min is -81 and it's x intercepts are 2 and =16

Don't pick D; it's min is -4 and the x intercepts are 2 and 6

Don't pick E; it has no x intercepts and the min is 2.

Don't pick F; it's min is -4, x intercepts are 2 and 6.

Answer 2

options A and B

Explanation:

We can evaluate the options using the given information:

Option A: When x = 2, f(2) = (2)^2 - 4(2) - 12 = 4 - 8 - 12 = -16 (matches the given minimum value).

Option B: When x = 2, f(2) = (2 - 2)^2 - 16 = 0 - 16 = -16 (matches the given minimum value).

Option C: When x = 2, f(2) = (2 - 2)(2 + 16) = 0 * 18 = 0 (does not match the given minimum value).

Option D: When x = 2, f(2) = (2 - 6)(2 - 2) = -4 * 0 = 0 (does not match the given minimum value).

Option E: When x = 2, f(2) = (2 - 6)^2 + 2 = (-4)^2 + 2 = 16 + 2 = 18 (does not match the given minimum value).

Option F: When x = 2, f(2) = (2)^2 - 8(2) + 12 = 4 - 16 + 12 = 0 (does not match the given minimum value).

Based on the analysis, options A and B are the only ones that match the given information. Therefore, the equivalent forms of the function f(x) are A. f(x) = x^2 - 4x - 12 and B. f(x) = (x - 2)^2 - 16.