SOLUTION: f(x)=-2x^2+2x+6 1.) What is the x-coordinate of the vertex? 2.) What is the y-coordinate of the vertx? 3.) The equation of the line of symmetry is x=______ 4.) The maximum/mini

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: f(x)=-2x^2+2x+6 1.) What is the x-coordinate of the vertex? 2.) What is the y-coordinate of the vertx? 3.) The equation of the line of symmetry is x=______ 4.) The maximum/mini      Log On


   

Question 287907: f(x)=-2x^2+2x+6
1.) What is the x-coordinate of the vertex?
2.) What is the y-coordinate of the vertx?
3.) The equation of the line of symmetry is x=______
4.) The maximum/minimum of f(x) is ________
5.) The value f(1/2)=13/2 is minimum or maximum?
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
The general form for the equation of a parabola is
f%28x%29+=+ax%5E2+%2B+bx+%2Bc
So your "a" is -2, your "b" is 2 and your "c" is 6. Use these numbers below:

1.) What is the x-coordinate of the vertex?
The x-coordinate of the vertex is %28-b%29%2F2a

2.) What is the y-coordinate of the vertex?
Put the value of %28-b%29%2F2a into the function for x and calculate y/f(x)

3.) The equation of the line of symmetry is x= %28-b%29%2F2a

4.) The maximum/minimum of f(x) is the: vertex

5.) The value f(1/2)=13/2 is minimum or maximum?
Since the "a" is negative, this parabola opens downward. So the vertex is a maximum value. If the point (1/2, 13/2) is the vertex, which you should know from #1 and #2 above, then it is the maximum value for f(x).