All you need is on the photo this is a homework

We have the quadratic function:

1) We have to factorize it in this way:

To do that we have to find the roots x1 and x2.

We can apply the quadratic formula as:

We have the values of both of the roots, so we can factorize f(x) as:

2) We have to express f(x) in vertex form.

To do that we can rearrange the expression as:

The vertex form for f(x) is:

3)

a) The x-intercepts are the roots of the function: x1=-2 and x2=6. For this values of x, the function has a value of 0. X-intercepts can be expressed as (-2,0) and (6,0).

b) The y-intercept is given by the independent value in the equation, c=-12. The is the value of the function when x=0, that is, f(0)=-12. It can be expressed as (0,-12).

c) The vertex is (2,-16) and can be deduced from the vertex expression f(x)=(x-2)^2-16.

d) The axis of symmetry, as it is a parabola, is a vertical axis that pass through the vertex. Then, its definition is x=2, as the vertex is at (2,-16).

e) The quadratic funtion in this case, as the quadratic coefficient is positive, has a minimum.

f) The minimum is located at the vertex and has a value of y=-16.

the first one

step-by-step explanation:

just id the test.