Question

How do you write the equation of the parabola in vertex form given vertex (-3,4); x-intercept -1?

Answer 1

`y=-(x+3)^2+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)=(-3,4)`

`rArry=a(x+3)^2+4`

`"x-intercept is -1 "rArr(-1,0)" is a point on the parabola"`

`"using " (-1,0)" to find a"`

`0=a(-1+3)^2+4`

`rArr4a+4=0rArra=-1`

`rArry=-(x+3)^2+4larrcolor(red)" equation in vertex form"`
graph{-(x+3)^2+4 [-10, 10, -5, 5]}