Question

How do you write a quadratic equation with y-intercept of -4 and vertex at (3, -7)?

Answer 1

`y=1/3x^2-2x-4`

Explanation:

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

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

`"here " (h,k)=(3,-7)`

`rArry=a(x-3)^2-7`

`"to find a, use y-intercept of - 4"rarr(0,-4)`

`-4=9a-7`

`rArra=1/3`

`rArry=1/3(x-3)^2-7larrcolor(red)" in vertex form"`

`"distributing and simplifying gives"`

`y=1/3(x^2-6x+9)-7`

`rArry=1/3x^2-2x-4larrcolor(red)" in standard form"`