Question

What is the vertex of the quadratic function f(x)=(x-6)(x+2)

Answer 1

(2,-16) should be the correct answer..

Answer 2

For this case we have the following function:

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

We rewrite the function making distributive property.

We have then:

$f (x) = x ^ 2 + 2x - 6x - 12 f (x) = x ^ 2 - 4x - 12$

To find the vertex of the function, we derive:

$f '(x) = 2x - 4$

We equal zero and clear the value of x:

$2x - 4 = 0 2x = 4$

$x = \frac{4}{2} x = 2$

We evaluate the function for the value of x obtained:

$f (2) = (2) ^ 2 - 4 (2) - 12 f (2) = 4 - 8 - 12 f (2) = -16$

Then, the vertice of the parabola is:

$(x, y) = (2, -16)$

Answer:

the vertex of the quadratic function f(x)=(x-6)(x+2) is:

$(x, y) = (2, -16)$