SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function of f(x)=2x^2 - 12x + 18. a. Type an ordered pair. b. What

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function of f(x)=2x^2 - 12x + 18. a. Type an ordered pair. b. What       Log On


   

Question 211893: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function of f(x)=2x^2 - 12x + 18.
a. Type an ordered pair.
b. What is the equation of the line of symmetry? x = _____
c. What is the maximum/minimum of f(x)?
d. Is the value, f(3)=0 a minimum or a maximum?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
For the quadratic equation, f%28x%29+=+2x%5E2-12x%2B18 find:
a. The vertex.
The x-coordinate of the vertex can be found by:
x+=+%28-b%29%2F2a where a = 2 and b = -12.
x+=+%28-%28-12%29%29%2F2%282%29 Evaluate:
x+=+3 Now substitute this into the given equation and solve for y (f(x)).
y+=+2%283%29%5E2-12%283%29%2B18
y+=+18-36%2B18
y+=+0
The ordered pair of the vertex is: (3, 0)
b. The equation of the line of symmetry is:
x+=+3
cand d. The maximum/minimum value of f(x) is found at the vertex (3, 0),
so f(3) = 0 and, because the coefficient of the x%5E2 term is positive (2), the parabola opens upward so this is a minimum.
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2x%5E2-12x%2B18%29