Question

Pls do not answer if you do not know the answer. I have had this problem many times and do not want to report anyone today. 45 points.

The quadratic function f(x) has roots of -2 and 6, and it passes through the point (1, 15).
What is the vertex form of the equation of f(x)?

f(x) = (x - 2)² +16
f(x) = (x + 2)² + 16
f(x) = -(x - 2)² + 16 f
(x) = -(x + 2)² + 16​

Answer 1

To find the vertex form of the quadratic equation, we need to first find the equation in standard form, which is:

f(x) = a(x - r)(x - s)

where r and s are the roots of the quadratic equation and a is a constant.

From the problem statement, we know that the roots of the quadratic equation are -2 and 6. Thus, we can write:

f(x) = a(x + 2)(x - 6)

To find the value of a, we can use the point (1, 15) that the function passes through. We substitute x = 1 and f(x) = 15 into the equation:

15 = a(1 + 2)(1 - 6)

15 = -15a

Thus, a = -1.

Substituting this value of a into the equation, we get:

f(x) = -(x + 2)(x - 6)

To convert this equation into vertex form, we need to complete the square. We can do this by adding and subtracting (2/2)² = 1 from the equation:

f(x) = -(x + 2)(x - 6) + 1 - 1

= -(x + 2)² + 16

Therefore, the vertex form of the equation of f(x) is f(x) = -(x + 2)² + 16.

Explanation:

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