SOLUTION: I have to complete the square to change the form of the function and grph the quadractic function???? f(x) = -2x^2 -5x +1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I have to complete the square to change the form of the function and grph the quadractic function???? f(x) = -2x^2 -5x +1      Log On


   

Question 468430: I have to complete the square to change the form of the function and grph the quadractic function????
f(x) = -2x^2 -5x +1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = -2x^2 - 5x + 1
:
-2x^2 - 5x + ___ = -1
divide by -2, change the signs
x^2 + 5%2F2x + ___ = 1%2F2
:
Find the term that will complete the square, add to both sides
Divide the coefficient of x by 2 and square it (5/4)^2 = 25/16
x^2 + 5%2F2x + 25%2F16 = 1%2F2 + 25%2F16
:
x^2 + 5%2F2x + 25%2F16 = 8%2F16 + 25%2F16
:
x^2 + 5%2F2x + 25%2F16 = 33%2F16
:
(x + 5%2F4)^2 = 33%2F16
:
x + 5%2F4 = +/- sqrt%2833%2F16%29
Two solutions
x = -5%2F4 + 1%2F4sqrt%2833%29
x = %28-5+%2B+sqrt%2833%29%29%2F4
and
x = -5%2F4 - 1%2F4sqrt%2833%29
x = %28-5+-+sqrt%2833%29%29%2F4
:
:
The graph
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-2x%5E2-5x%2B1%29+