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

##### 1 Answer

Jun 30, 2018

#### 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]}