Question

Find a quadratic function associated with the vertex (h,k)=(2,1) and point (x,y)=(6,7) that the parabola passes through.

Answer 1

you've covered parabolas I assume?

Answer 2

Yes.

Answer 3

well I use the standard form

(x - h)^2 = 4a(y - k)

(h, k) is the vertex

so substitute those values...

then substitute the point to find the value of a.

then you have the equation...

to get it to vertex form is simply a case of making y the subject

Answer 4

Okay, thanks!

Answer 5

ok so we know the vertex is at (2,1) \(\bf y=a(x-{\color{brown}{ h}})+{\color{blue}{ k}}\qquad vertex\ ({\color{brown}{ 2}},{\color{blue}{ 1}})\implies y=a(x-{\color{brown}{ 2}})+{\color{blue}{ 1}}\)

Answer 6

well.. using campbell_st's will work the same :)

Answer 7

and use the vertex template, with the vertex coordinates

and since the line passes through (6,7) meaning x =6, y =7

then just plug that in the vertex form and solve for "a"

to find that factor

then plug it back in the equation