SOLUTION: can you help me with this problem? A parabola is congruent to y=x^2 and has x-intercepts 1 and 5. determine the coordinates of the vertex

Algebra ->  Rational-functions -> SOLUTION: can you help me with this problem? A parabola is congruent to y=x^2 and has x-intercepts 1 and 5. determine the coordinates of the vertex      Log On


   

Question 117324: can you help me with this problem? A parabola is congruent to y=x^2 and has x-intercepts 1 and 5. determine the coordinates of the vertex
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A parabola is symmetric about the vertex.
If you take the average of the x intercepts you will find the x coordinate of the parabola.
x%5Bv%5D=%281%2B5%29%2F2
x%5Bv%5D=3
The general equation, congruent to y=x%5E2, is then,
y=%28x-3%29%5E2%2By%5B0%5D
Find y%5B0%5D by using either point,
0=%285-3%29%5E2%2By%5B0%5D
y%5B0%5D=-4
y=%28x-3%29%5E2-4
The vertex is (3,-4).
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C+%28x-3%29%5E2-4%29+%29