I need help with some of my college algebra math homework.?

Question

-The x-coordinate of the vertex of the parabola f(x)=-2-x+x^2 is?

-f(x)=2x^2+4, g(x)=x+3
A) 46
B)-28
C)64
D)28

-f(x)=x+5, g(x)=x-5
Find (f+g)(-5)
A)-15
B)-5
C)-10
D)0

-f(x)=2x-4, g(x)=4x-9
Find (fg)(x)
A)8x^2-x+36
B)8x^2-34x+36
C)8x^2+36
D)6x^2-34x+1

Answer 1

(1).

The parabola equation is f(x) = - 2 - x + x².

Compare the above equation with general form of parabola equation f(x) = ax² + bx + c.

a = 1, b = -1 and c = -2.

The x coordinate of vertex is axis of symmetry x = - b/2a = -(-1)/2(1) = 1/2.

Answer 2

(3).

The functions are f(x) = x + 5 and g(x) = x - 5.

(f+g)(x) = f(x) + g(x) = (x + 5) + (x - 5) = 2x.

(f+g)(-5) = 2(-5) = - 10.

The option C is correct.

 

Answer 3

(4).

The functions are f(x) = 2x - 4 and g(x) = 4x - 9.

(f*g)(x) = f(x) * g(x) = (2x - 4)(4x - 9) = 8x² - 18x -16x + 36 = 8x² - 34x + 36.

The option B is correct.