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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).

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Answer:

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.

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