v=(-2,-5), point=(-6,0)

Question

writing equations of parabola's in vertex form

Answer 1

The vertex form for a parabola is:

 

y = a(x-h)² + k

 

where (x,y) is any point on the parabola, (h,k) is the vertex, and a is a constant. So in this problem, (h,k) = (-2, -5).

 

So far this gives us the equation:

 

y = a[x - (-2)]² + (-5)

 

OR

 

y = a(x+2)² - 5

 

To get the final equation, we need to figure out what the constant a is. We do this by plugging in a point on the parabola and solving for a. And the point we are given is (-6,0). So:

 

y = a(x+2)² - 5

0 = a(-6 + 2)² - 5

0 = a(-4)² - 5

0 = 16a - 5

5 = 16a

a = 5/16

 

Thus, our final equation in vertex form is:

 

y = 5/16(x + 2)² - 5