SOLUTION: Find the vertex of f(x) = x^2-10x+21. Is the vertex the maximum or minimum value of f? How do you know?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the vertex of f(x) = x^2-10x+21. Is the vertex the maximum or minimum value of f? How do you know?      Log On


   

Question 202262: Find the vertex of f(x) = x^2-10x+21. Is the vertex the maximum or minimum value of f? How do you know?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex of:
f%28x%29+=+x%5E2-10x%2B21
The x-coordinate of the vertex is given by:
x+=+%28-b%29%2F2a and in this problem, a = 1, b = -10, so...
x+=+-%28-10%29%2F2%281%29
x+=+5 To find the y-coordinate, substitute this into the given quadratic equation and solve for y (f(x)).
y+=+x%5E2-10x%2B21 Substitute x = 5.
y+=+5%5E2-10%285%29%2B21 Evaluate.
y+=+25-50%2B21
y+=+-4
The vertex is at (5, -4)
This is a minimum point on the curve because the positive value of the x%5E2 coefficient indicates that the parabola opens upwards.
graph%28400%2C400%2C-5%2C10%2C-5%2C5%2Cx%5E2-10x%2B21%29