Write the equation of the parabola

Question

Write the equation of the parabola in vertex form given the vertex: (1/4, -3/2) and point (1,3)

Answer 1

The vertex form is:

 

y = a(x-h)² + k

 

where (h,k) is the location of the vertex.  We are told that the vertex lies at (1/4,-3/2); so h = 1/4 and k = -3/2:

 

y = a(x - 1/4)² - 3/2

 

To find a, plug in the value of the known point, (1,3), and solve for a:

 

3 = a(1 - 1/4)² - 3/2

9/2 = a(3/4)²

9/2 = a(9/16)

8 = a

 

y = 8(x - 1/4)² - 3/2