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.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

i only know the sequence of arithmetic it adds the first is 5+4 then it goes up as it adds to then it is 9+5 then 14+6 then to 20+7 and so on. 5,9,14,20,27,35.

step-by-step explanation: