# What is the equation of the parabola with a vertex of (8,3) and an x intercept of 5?

Jan 30, 2016

$y = - \frac{1}{3} {\left(x - 8\right)}^{2} + 3$

#### Explanation:

The vertex form of the equation is :

$y = a {\left(x - h\right)}^{2} + k$

where ( h , k ) are the coords of the vertex.

using (8 , 3) : $y = a {\left(x - 8\right)}^{2} + 3$

To find a , requires another point. Given that the

x-intercept is 5 then point is (5 , 0 ) as y-coord is 0 on x-axis.

Substitute x = 5 , y = 0 into equation to find value of a.

<hence  a(5-8)^2 + 3 = 0 → 9a = - 3 → a = -1/3

equation is then # y = -1/3 (x - 8 )^2 + 3

graph shows vertex at (8,3) and x-intercept of 5 .

graph{-1/3(x-8)^2 +3 [-11.25, 11.25, -5.625, 5.625]}