Question

What is the equation of the parabola that has a vertex at `(14, -9)` and passes through point `(0, 2)`?

Answer 1

`y=11/196(x-14)^2-9`

Explanation:

The equation of a parabola in `color(blue)"vertex form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=a(x-h)^2+k)color(white)(a/a)|)))`
where (h ,k) are the coordinates of the vertex and a, is a constant.

here h = 14 and k = - 9, so we can write a partial equation

`y=a(x-14)^2-9`

To find a, substitute the coordinates of (0 ,2) a point on the parabola, into the partial equation.

`rArra(0-14)^2-9=2rArr196a=11rArra=11/196`

`rArry=11/196(x-14)^2-9" is equation in vertex form"`

The equation may be expressed in `color(blue)"standard form"`

That is `y=ax^2+bx+c` by distributing the bracket and simplifying.

`rArry=11/196(x^2-28x+196)-9=11/196x^2-11/7x+2`

graph{11/196(x-14)^2-9 [-20, 20, -10, 10]}