Question

Put the quadratic equation y=4x^2-24x+5 into vertex form by completing the square then state the coordinates of the vertex.

Answer 1

(3, -31)

Explanation:

Factor 4 out of the first two terms:

y=4x^2-24x+5 becomes y=4(x^2 - 6x) +5

Next, complete the square of (x^2 - 6x): It is x^2 - 6x + 9 - 9

Insert this into y=4(x^2 - 6x) +5 in place of x^2 - 6x:

y=4(x^2 - 6x) +5 => y=4(x^2 - 6x + 9 - 9) +5, or

y=4( (x - 3)^2 - 9 ) + 5, or

y = 4(x - 3)^2 - 36 + 5, or:

y = 4(x - 3)^2 - 31

Compare this to: y = a(x - h)^2 + k

We see that the coordinates of the vertex (h, k) are (3, -31), and that a = 4.