Question

How do you write a quadratic function in vertex form whose has vertex (-1/2, 2/3) and passes through point (3/2, 14/3)?

Answer 1

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

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 multiplier"`

`"here "(h,k)=(-1/2,2/3)`

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

`"to find a substitute "(3/2,14/3)" into the equation"`

`14/3=4a+2/3rArr4a=4rArra=1`

`rArry=(x+1/2)^2+2/3larrcolor(blue)"in vertex form"`