Question

How do you write a quadratic equation with vertex; ( -2,-3 ); point: ( -3,-5 )?

Answer 1

`y=-2x^2-8x-11`

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)=(-2,-3)`

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

`"to find a substitute " (-3,-5)" into the equation"`

`-5=a-3rArra=-2`

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

`"distributing gives"`

`y=-2x^2-8x-8-3`

`rArry=-2x^2-8x-11larrcolor(red)" in standard form"`
graph{-2x^2-8x-11 [-12.66, 12.65, -6.33, 6.33]}