# Thread: vertex of the parabola y = 3x2 – 9x + 12, using the formulas for h and k.

1. ## vertex of the parabola y = 3x2 – 9x + 12, using the formulas for h and k.

Find the vertex of the parabola y = 3x2 – 9x + 12, using the formulas for h and k.

a.(-3/2,21/4)

b.(-3/2,-75/4)

c. (-3/2,129/4)

d. (3/2,21/4)

e. none of the above

thank you!!

3. Originally Posted by skylitejdm
Find the vertex of the parabola y = 3x2 – 9x + 12, using the formulas for h and k.

a.(-3/2,21/4)

b.(-3/2,-75/4)

c. (-3/2,129/4)

d. (3/2,21/4)

e. none of the above

thank you!!

Hi sky,

What we want to do is put your general equation into vertex form. Let's factor out a 3 from your first two terms like this:

$y=3x^2-9x+12$

$y=3(x^2-3x)+12$

Next, we'll complete the square with what we have inside the parentheses:

$y=3\left(x^2-3x+\frac{9}{4}\right)+12-\frac{27}{4}$

Finally, will arrage the above into vertex form.

$y=3\left(x-\frac{3}{2}\right)^2+\frac{21}{4}$

Vertex form is $y=a(x-h)^2+k$ where (h, k) is the vertex of the parabola.

That would make your vertex $\left(\frac{3}{2}, \frac{21}{4}\right)$