# What is the equation of the parabola with a vertex at (2,3) and zeros at x=0 and x=4?

##### 1 Answer

Dec 13, 2015

Find the equation of parabola

Ans:

#### Explanation:

General equation:

Equation passes at vertex --> 3 = (4)a + 2b + c (1)

y-intercept is zero, then c = 0 (2)

x- intercept is zero, --> 0 = 16a + 4b (3)

Solve system:

(1) --> 3 = 4a + 2b --> b = (3 - 4a)/2

(3) --> 16a + 4b = 0 --> 16a + 6 - 8a = 0 --> 8a = -6 --> a = -3/4.

b = (3 + 3)/2 = 3

Equation:

Check.

x = 0 --> y = 0 .OK

x = 4 --> y = -12 + 12 = 0. OK