Question

1. Given the following quadratic function: f(x)=4x2-12x+5

a. Use the method of completing the square to rewrite the equation of f

b. What are the coordinate of the vertex of f

c. What are the zeros of f (ker(f))

d. What is the image of f (image(f))

e. Describe the simple transformations that take x2 to f(x)

Answer 1

f(x) = 4x^2 + 12x +5.

a).f(x) = 4x^2 + 12x + 9 - 9 + 5.

f(x) = (4x^2 + 12x + 9) - 4.

f(x) = (2x + 3) ^ 2 - ( 2) ^ 2.

f(x) = (2x + 3 + 2) (2x + 3 - 2).

f(x) = (2x + 5)(2x +1).

b). coordinate of vertex of f is ( -5/2 , 0) and (-1/2 , 0).

c).zeros of f are -5/2 and -1/2.

d). the images of these points remain same because these points lies on x - axis and the image of points on the any axis is remain that point.

e).simple transformation of x^2 in f(x) is

f(x^2) = 4(x^2)^2 + 12(x^2) + 5.

f(x^2) = 4(x^4) + 12(x^2) + 5.