Question

How do you write a quadratic equation with vertex (2,1) y intercept (0,-3)?

Answer 1

`y=-x^2+4x-3`

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)=(2,1)`

`rArry=a(x-2)^2+1`

`"to find a, substitute " (0,-3)" into the equation"`

`-3=4a+1`

`rArr4a=-4rArra=-1`

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

`"distributing and simplifying gives"`

`y=-(x^2-4x+4)+1`

`color(white)(y)=-x^2+4x-4+1`

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