SOLUTION: Determine the maximum or minimum range value [P(x)] of the function P(x) = -3x2 + 6x + 5. State whether this value is a maximum or a minimum.

Algebra ->  Graphs -> SOLUTION: Determine the maximum or minimum range value [P(x)] of the function P(x) = -3x2 + 6x + 5. State whether this value is a maximum or a minimum.      Log On


   

Question 89994: Determine the maximum or minimum range value [P(x)] of the function P(x) = -3x2 + 6x + 5. State whether this value is a maximum or a minimum.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the maximum or minimum range value of the function:
P%28x%29+=+-3x%5E2%2B6x%2B5
First, since the coefficient of the x%5E2 term is <0 (negative), the parabola described by the functions opens downward so you know that the vertex will occur at the maximum.
To find the x-coordinate of the vertex, use:
x+=+-b%2F2a in this equation, a = -3, and b = 6.
x+=+-6%2F2%28-3%29
x+=+1 Now substitute this value of x into the quadratic equation and solve for y to get the y-coordinate of the vertex.
y+=+-3%281%29%5E2%2B6%281%29%2B5 Simplify.
y+=+-3%2B6%2B5
y+=+8
The vertex is at (1, 8) and is a maximum.
graph%28300%2C200%2C-5%2C5%2C-5%2C10%2C-3x%5E2%2B6x%2B5%29