Question

How do you find the quadratic function with vertex (-1/4, 3/2) and point (-2,0)?

Answer 1

`y=-24/49(x+1/4)^2+3/2`

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)=(-1/4,3/2)`

`y=a(x+1/4)^2+3/2`

`"to find a substitute "(-2,0)" into the equation"`

`0=a(-7/4)^2+3/2=49/16a+3/2`

`a=-3/2xx16/49=-24/49`

`y=-24/49(x+1/4)^2+3/2larrcolor(red)"in vertex form"`