What's its equation?

Question

A parabola has a minimum point at (-2,-5) and passing through (1,4). What's its equation?

Answer 1

The vertex form of a parabola is:

 

y  = a(x-x₁) + y₁  where (x₁,y₁) is the vertex so we get

 

y = a(x+2)² -5  now substitute our 2nd point for x and y and solve for a

 

4 = a(1+2)² - 5

 

9 = 9a

 

a =1

Answer 2

If (-2,-5) is the minimum, it is the vertex of the parabola.  Use the vertex form y = a(x-h)²+k where (h,k) is the location of the vertex = (-2,-5):

 

y = a(x-(-2)) + (-5)

y = a(x+2)² -5

 

To find a, plug in the given point (1,4):

 

y = a(x+2)² -5

4 = a(1+2)² -5

 

Solve for a.