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

Jun 30, 2018

$y = - \frac{3}{4} {x}^{2} + 3 x$

Explanation:

$\text{using the "color(blue)"intercept form}$

•color(white)(x)y=k(x-a)(x-b)

$\text{where a and b are the zeros and k is a multiplier}$

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

$\text{to find k substitute "(2,3)" into the equation}$

$3 = 2 k \left(- 2\right) \Rightarrow - 4 k = 3 \Rightarrow k = - \frac{3}{4}$

$y = - \frac{3}{4} x \left(x - 4\right) = - \frac{3}{4} {x}^{2} + 3 x$
graph{-3/4x^2+3x [-10, 10, -5, 5]}