Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

find the x-intercept of the parabola with vertex (6,27) and y-intercept (0,-81)

Sagot :

naǫ
The vertex form of the equation of a parabola with the vertex (h,k):
[tex]y=a(x-h)^2+k[/tex]

The parabola has the vertex at (6,27).
[tex]y=a(x-6)^2+27[/tex]

The y-intercept is (0,-81).
[tex]x=0, \ y=-81 \\ \Downarrow \\ -81=a(0-6)^2+27 \\ -81=a(-6)^2+27 \\ -81=36a+27 \\ -81-27=36a \\ -108=36a \\ \frac{-108}{36}=a \\ a=-3[/tex]

The equation of the parabola is:
[tex]y=-3(x-6)^2+27[/tex]

y=0 at the x-intercepts.
[tex]0=-3(x-6)^2+27 \\ -27=-3(x-6)^2 \\ \frac{-27}{-3}=(x-6)^2 \\ 9=(x-6)^2 \\ \sqrt{9}=\sqrt{(x-6)^2} \\ 3=|x-6| \\ x-6=3 \ \lor \ x-6=-3 \\ x=3+6 \ \lor \ x=-3+6 \\ x=9 \ \lor \ x=3[/tex]

The x-intercepts are x=3 and x=9.

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.