Question

How do you write a quadratic function in vertex form whose graph has the vertex `(1, 8)` and passes through the point `(3, 12)`?

Answer 1

`y=(x-1)^2+8`

Explanation:

`"the equation of a quadratic 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)=(1,8)`

`y=a(x-1)^2+8`

`"to find a substitute "(3,12)" into the equation"`

`12=4a+8`

`12-8=4arArr4a=4rArra=1`

`y=(x-1)^2+8larrcolor(red)"in vertex form"`
graph{(x-1)^2+8 [-28.87, 28.86, -14.43, 14.44]}