Question

Help!!
Find a function whose graph is a parabola with vertex (3, 5) and that passes through the point (2, −9).

Answer 1

do you know the vertex form of a parabola?

Answer 2

No

Answer 3

http://www.mathwarehouse.com/geometry/parabola/images/standard-vertex-forms-thumb.png

Answer 4

\(\bf y={\color{olive}{ a}}(x-{\color{brown}{ h}})^2+{\color{brown}{ k}}\qquad vertex \ ({\color{brown}{ 3,5}})\implies y={\color{olive}{ a}}(x-{\color{brown}{ 3}})^2+{\color{brown}{ 5}}
\\ \quad \\
\textit{what's }{\color{olive}{ a}}?\qquad \textit{well we dunno, but we know it passes through }(2,-9)
\\ \quad \\
thus \qquad (2,-9)\to x=2\quad y=-9\qquad -9={\color{olive}{ a}}(2-{\color{brown}{ 3}})^2+{\color{brown}{ 5}}\)

solve for "a" to find that factor, and plug it back in the equation

Answer 5

-14(x-3)^2+5?

Answer 6

yeap

Answer 7

Thanks!!!

Answer 8

yw