Question

How do you write the quadratic equation given Vertex: (3,-11) Passing though: (5,2)?

Answer 1

`y=13/4x^2-39/2x+73/4`

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) is the vertex and a, a constant.

`"here " (h,k)=(3,-11)`

`rArry=a(x-3)^2-11" is the partial equation"`

To find a, substitute the point (5 ,2) into the equation.

`2=a(5-3)^2-11`

`rArr2=4a-11`

`rArra=(2+11)/4=13/4`

`rArry=13/4(x-3)^2-11larrcolor(red)" in vertex form"`

distributing and simplifying gives.

`y=13/4x^2-39/2x+73/4larrcolor(red)" in standard form"`