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

Solution:

We have to find the vertex of the quadratic function.

For any equation of the type y = ax² + bx + c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is f(x) = (x - 6)(x + 2)

f(x) = x² - 6x + 2x - 12

f(x) = x² - 4x - 12

Here, a = 1, b = -4 and c = -12

So, h = -(-4)/2(1)

h = 4/2

h = 2

4ac = 4(1)(-12)

4ac = -48

So, k = [-48 - (-4)²]/4(1)

k = (-48 - 16)/4

k = -64/4

k = -16

Therefore, the vertex is (h, k) = (2, -16).

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

Summary:

The vertex of the quadratic function f(x) = (x - 6)(x + 2) is (2, -16).