Question

How do you find parabola equation given vertex is (2,3) and the zeros are x=0 and x=4?

Answer 1

`y=-3/4x^2+3x`

Explanation:

`"using the "color(blue)"intercept form"`

`•color(white)(x)y=k(x-a)(x-b)`

`"where a and b are the zeros and k is a multiplier"`

`"y=k(x-0)(x-4)=kx(x-4)`

`"to find k substitute "(2,3)" into the equation"`

`3=2k(-2)rArr-4k=3rArrk=-3/4`

`y=-3/4x(x-4)=-3/4x^2+3x`
graph{-3/4x^2+3x [-10, 10, -5, 5]}