College Algebra

Question

Find the vertex of the parabola f(x) = x2 - 16x + 63.

Find the x- and y-intercepts of the cubic function f(x) = (x+4)(2x-1)(x-1).

If f(x) = x2-2x-24 and g(x) = x2-x-30, find (f-g)(x).

If f(x) = x+4 and g(x) = 2x2-x-1, evaluate the composition (g o f)(2).

If f(x) = x+4 and g(x) = 2x2-x-1, find the composition (f o g)(x).

Answer 1

I'm in a good mood because the Colts won today; So, I'm going to do all of these for you. :)

1) f(x) = x² - 16x + 63

x = -b/2a = 16/2 = 8

y = 8² -16(8) + 63 = 64 - 128 + 63

y = -1

V(8,-1)

 

2) f(x) = (x+4)(2x-1)(x-1)

x + 4 = 0      2x - 1 = 0         x - 1 = 0

      x = -4          2x = 1              x = 1

                           x = 1/2

 

3) f(x) = x² - 2x - 24    and g(x) = x² - x - 30

(f-g)(x) = x² - 2x - 24 - (x² - x -30)

(f-g)(x) = x² - 2x - 24 - x² + x + 30

(f-g)(x) = -x + 6

 

4) f(x) = x + 4    and g(x) = 2x² - x - 1      * is going to stand for composite

(g*f)(x) = 2(x+4)² - (x+4) -1 = 2(x² + 8x + 16) - x - 4 - 1 = 2x² + 16x + 32 - x - 5 = 2x² + 15 x + 27

(g*f)(2) = 2(2)² + 25(2) + 27 = 65

 

5) f(x) = x + 4 and g(x) = 2x² - x - 1

(f*g)(x) = 2x² - x - 1 + 4 = 2x² - x + 3

 

You can thank the Colts for inspiring all of these answers.