SOLUTION: f(x)=-3x^2+3x-2 a. opens b. vertex = (-0.5,-2.75) c axis of symmetry x=-0.5 d. show algebraically how you know the function has no x-intercepts - it does x-intercepts of -1.

Algebra ->  Functions -> SOLUTION: f(x)=-3x^2+3x-2 a. opens b. vertex = (-0.5,-2.75) c axis of symmetry x=-0.5 d. show algebraically how you know the function has no x-intercepts - it does x-intercepts of -1.      Log On


   

Question 1157403: f(x)=-3x^2+3x-2
a. opens
b. vertex = (-0.5,-2.75)
c axis of symmetry x=-0.5
d. show algebraically how you know the function has no x-intercepts - it does x-intercepts of -1.457 and 0.457
e internal where it is increasing and decreasing
Decreasing (-inf, -0.5) Increasing (0.5, inf)
Found 2 solutions by MowMow, ikleyn:
Answer by MowMow(42) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=-3x^2+3x-2
a. opens
b. vertex = (-0.5,-2.75)
c axis of symmetry x=-0.5
d. show algebraically how you know the function has no x-intercepts - it does x-intercepts of -1.457 and 0.457
e internal where it is increasing and decreasing
Decreasing (-inf, -0.5) Increasing (0.5, inf)

Answer by ikleyn(52750) About Me  (Show Source):
You can put this solution on YOUR website!
.

graph%28+330%2C+330%2C+-3%2C+3%2C+-10%2C+4%2C%0D%0A++++++++++-3x%5E2%2B3x-2%0D%0A%29


Plot y = -3x%5E2%2B3x-2



(a)  Opens downward  (since the leading coefficient is negative).


(b)  Vertex  x = -3%2F%282%2A%28-3%29%29 = 0.5.

             y = -3*0.5^2 + 3*(0.5) - 2 = -1.25.


(c)  axis of symmetry:  x = 0.5.


(d)  It is opened downward and has negative maximum  --- H E N C E, there is NO x-intercepts.


     It is clear LOGICALLY and VISUALLY, but if you want algebraic confirmation, calculate the DISCRIMINANT of the equation
     to assure that it is NEGATIVE.


(e)  increases at (-oo,0.5).  Decreases at (0.5,oo).


As you see, my answers ALL are opposite to yours.


All answers in your post are INCORRECT.   (All means EACH and EVERY).