Question

How do you write a quadratic equation with vertex (2,-4) and the point (1,-1)?

Answer 1

`y=3x^2-12x+8`

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 multiplier"`

`"here "(h,k)=(2,-4)`

`rArry=a(x-2)^2-4`

`"to find a substitute "(1,-1)" into the equation"`

`-1=a-4rArra=-1+4=3`

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

`"distributing and simplifying gives"`

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

`rArry=3x^2-12x+8larrcolor(red)"equation in standard form"`