SOLUTION: Your help is appreciated. Convert equation of the parabola y = -6x^2-6x to standard form and then find the product a x h x k. Thank you.

Algebra ->  Graphs -> SOLUTION: Your help is appreciated. Convert equation of the parabola y = -6x^2-6x to standard form and then find the product a x h x k. Thank you.      Log On


   

Question 13406: Your help is appreciated.
Convert equation of the parabola y = -6x^2-6x to standard form and then find the product a x h x k.
Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The "standard" form you need for this problem is:
f%28x%29+=+a%28x+-+h%29%5E2+%2B+k
You can get your equation into this form by "completing the square".
Starting with your equation, factor a (-6), then complete the square in the x-terms:
y+=+-6x%5E2+-+6x Factor -6
y+=+-6%28x%5E2+%2B+x%29 Complete the square in x by adding the square of half the x-term (1/2)^2 = 1/4 but don't forget that this is multiplied by -6 so you must add -6(1/4)= -3/2 to the other side as well.
y+-+3%2F2+=+-6%28x%5E2+%2B+x+%2B+%281%2F4%29%29Factor the parentheses and add 3/2 to both sides.
y+=+-6%28x+%2B+%281%2F2%29%29%5E2+%2B+%283%2F2%29 Now compare this with the "standard" form:
y+=+a%28x+-+h%29%5E2+%2B+k and you can see that:
a = -6, h = -(1/2), and k = 3/2
So, to finish the solution to your problem:
a%2Ah%2Ak+=+%28-6%29%28-1%2F2%29%283%2F2%29 = 9/2 = 4.5