Question

How do you write the quadratic equation given Vertex: (1/2, 1/2) Passing though: (3/4, 1/4)?

Answer 1

`y=-4x^2+4x-1/2`

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 constant.

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

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

`"to find a substitute "(3/4,1/4)" into the equation"`

`1/4=1/16a+1/2rArra=-4`

`rArry=-4(x-1/2)^2+1/2larrcolor(red)" in vertex form"`

`rArry=-4x^2+4x-1/2larrcolor(red)" in standard form"`