A parabola has a vertex at (2,4). The y-coordinate of the parabola at x=3 is 18/6 . Determine the x-intercepts of the parabola. Enter your answer in exact form

Question

I need to find what the smaller and larger x intercepts are, but I'm not sure how to do that (and it's a homework question with a topic that hasn't yet been covered in class) From what I've been discovering, I think that the x intercepts are 0 and 4, but I'm not sure.

Answer 1

A parabola in vertex form is

 

y = a(x - h)² + k

 

where:

a is the coefficient of x²

(x, k) is the vertex

 

y = a(x - 2)² + 4

 

 

Now we solve for a using the point (3, 3).

 

3 = a(3 - 2)² + 4

3 = a + 4

-1 = a

 

y = -(x - 2)² + 4

 

 

Now we use the vertex form to find the x-intercepts.

 

-(x - 2)² + 4 = 0

 

-(x - 2)² = -4

 

(x - 2)² = 4

 

 

Square-root both sides of the equation.

 

x - 2 = ±√4

 

x = 2 ± √4

 

x = 2 ± 2

 

x = 0   ----> minus sign

x = 4    ---->  plus sign