SOLUTION: What is the vertex of a parabola? How do you determine the vertex of the parabola? Demonstrate with an example.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: What is the vertex of a parabola? How do you determine the vertex of the parabola? Demonstrate with an example.      Log On


   

Question 332261: What is the vertex of a parabola?
How do you determine the vertex of the parabola?
Demonstrate with an example.
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
the equation for a parabola: y=a%2Ax%5E2%2Bb%2Ax%2Bc
The vertex is at x=-b%2F%282a%29, y=%284ac-b%5E2%29%2F%284a%29
--
this can be found from the quadratic solutions are
x=%28-b-Sqrt%28b%5E2-4ac%29%29%2F%282a%29 and
x=%28-b%2BSqrt%28b%5E2-4ac%29%29%2F%282a%29
--
The center is at value x=-b%2F%282a%29 and then substituting this x value in the parabola equation to find y
--
Try it: for parabola Y=2%2Ax%5E2%2B8%2Ax%2B11
x=-b%2F%282a%29 = -8/4=-2
y=%284ac-b%5E2%29%2F%284a%29 = (4*2*11-8^2)/(4*2) = 24/8=3
---
if you complete the square for Y=2%2Ax%5E2%2B8%2Ax%2B11
y=2%2A%28x%2B2%29%5E2+%2B3 for which it is easy to see that the vertex is (-2,3)