Pre calclulus quesiton? ANYONE HELP?

Question

h(x) = 8-10x^2

1) Find h(x+2)

2) Find (h(x+t) -h(x))/t

Answer 1

(1).

The function h(x) = 8 - 10x².

To find h(x + 2), substitute x = x + 2 in the above function.

h(x + 2) = 8 - 10(x + 2)²

              = 8 - 10(x² + 4x + 4)

              = 8 - 10x² - 40x - 40

h(x + 2) = - 10x² - 40x - 32.

Answer 2

(2).

The function h(x) = 8 - 10x².

To find h(x + t), substitute x = x + t in the above function.

h(x + t) = 8 - 10(x + t)²

              = 8 - 10(x² + 2xt + t²)

              = 8 - 10x² - 20xt - 10t²

 

h(x + t) - h(x) = 8 - 10x² - 20xt - 10t² - (8 - 10x²)

                       = 8 - 10x² - 20xt - 10t² - 8 + 10x²

                       = - 20xt - 10t²

                       = - 10t(2x + t)

 

[h(x + t) - h(x)] / t = [- 10t(2x + t)] / t

                              = - 10(2x + t)

                              = - 20x - 10t.

[h(x + t) - h(x)] / t = - 20x - 10t.