please help solve, thank you

Calculus
Tutor: None Selected Time limit: 1 Day

f(x) = -2x^2 + 18x

a. find vertex and determine whether it is a max or minimum

b. find zeros

c. Graph

Thank you!

Oct 3rd, 2015

Thank you for the opportunity to help you with your question!

a) f(x) = -2x^2 + 18x,  so comparing f(x) to ax^2 + bx + c, we have a = -2, b = 18, c = 0. The formula for the vertex is (-b/2a) which in this case means x = -18/2(-2) = 18/4 = 9/2 = 4.5. Because a < 0, the parabola opens downward, so at the vertex, f(x) is at its maximum.

b) Factoring f(x) and setting it equal to zero, we get -2x(x - 9) = 0. This is a true statement only if x = 0 or x = 9.

c) I'm having troubel with my plotter. The graph should look an open umbrella, kind of like an upside down U. It will cross the x-axis at x = 0 and x = 9 with a y-coordinate of zero at each of these two points.

quadratic.png 

I can do better than this, but you get the idea.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 22nd, 2015

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