SOLUTION: f(x)=-3x^2+3x-2 a. opens up or opens down b. vertex = c axis of symmetry d. show algebraically how you know the function has no x-intercepts e internal where it is increasin

Algebra ->  Functions -> SOLUTION: f(x)=-3x^2+3x-2 a. opens up or opens down b. vertex = c axis of symmetry d. show algebraically how you know the function has no x-intercepts e internal where it is increasin      Log On


   

Question 1157414: f(x)=-3x^2+3x-2
a. opens up or opens down
b. vertex =
c axis of symmetry
d. show algebraically how you know the function has no x-intercepts
e internal where it is increasing and decreasing
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

duplicate.

I just answered it. See the link

https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1157403.html



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=-3x%5E2%2B3x-2
a. opens up or opens down
opens+down=> coefficient of the+x%5E2 is negative
b. vertex =
write equation in vertex form
f%28x%29=%28-3x%5E2%2B3x%29-2
f%28x%29=-3%28x%5E2-x%29-2.......complete square
f%28x%29=-3%28x%5E2-x%2Bb%5E2%29-%28-3%29b%5E2-2.......b=1%2F2
f%28x%29=-3%28x%5E2-x%2B%281%2F2%29%5E2%29%2B3%281%2F2%29%5E2-2
f%28x%29=-3%28x%5E2-x%2B%281%2F2%29%5E2%29%2B3%281%2F2%29%5E2-2
f%28x%29=-3%28x-1%2F2%29%5E2%2B3%2F4%29-2
f%28x%29=-3%28x-1%2F2%29%5E2%2B3%2F4-8%2F4
f%28x%29=-3%28x-1%2F2%29%5E2-5%2F4
h=1%2F2,k=-5%2F4
vertex is at (1%2F2,-5%2F4)

c axis of symmetry
The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
x=1%2F2
d. show algebraically how you know the function has no x-intercepts
-3x%5E2%2B3x-2=0
If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.
if determinant <0
b%5E2-4ac%3C0
3%5E2-4%28-3%29%28-2%29%3C0
9-24%3C0
-15%3C0->proven


e. internal where it is increasing and decreasing
in interval (-infinity,1%2F2) is increasing ,and in interval (1%2F2,infinity) decreasing