Which of the following describes the parabola with the equation y = 4x2 - 12x + 9?

A) The axis of symmetry is x = 0 and the vertex is (0,9).

B) The axis of symmetry is x = 1.5 and the vertex is (1.5, 0).

C) The axis of symmetry is x = 4 and the vertex is (4, - 12).

D) The axis of symmetry is x = - 1.5 and the vertex is (-1.5, 36).

Step-by-step explanation:

To find the vertex of this parabola, "complete the square:" Rewrite y = 4x2 - 12x + 9 in the form y = 4 (x - h) ^2 + k:

y = 4x^2 - 12x + 9 = > y = 4 (x^2 - 3x) + 9.

Now complete the square of x^2 - 3x: Take half of - 3 and square the result, obtaining (-3/2) ^2, or 9/4. Add 9/4 to x^2 - 3x and then subtract 9/4 from the result: We get x^2 - 3x + 9/4 - 9/4. Substitute this result back into

y = 4 (x^2 - 3x) + 9: y = 4 (x^2 - 3x + 9/4 - 9/4) + 9

and then rewrite the perfect square x^2 - 3 + 9/4 as the square of a binomial:

y = 4 (x - 3/2) ^2 - 9/4) + 9. This simplifies to:

y = 4 (x - 3/2) ^2 + 0.

Thus, the vertex is at (3/2, 0) and the axis of symmetry is x = 3/2. This agrees with Answer B.