SOLUTION: Given the equation: f(x)=2x^2-3x+5 determine whether the graph opens up or down, the vertex of the equation, the axis of symmetry, y-intercepts and x intercepts, if and determine w

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given the equation: f(x)=2x^2-3x+5 determine whether the graph opens up or down, the vertex of the equation, the axis of symmetry, y-intercepts and x intercepts, if and determine w      Log On


   

Question 853902: Given the equation: f(x)=2x^2-3x+5 determine whether the graph opens up or down, the vertex of the equation, the axis of symmetry, y-intercepts and x intercepts, if and determine where the function is increasing and where it is decreasing.
Help would me be much appreciated. Very confused!
Thanks!
Found 2 solutions by josgarithmetic, gateau052706:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Most but not all of what you want is discussed here:

Completing the Square to Solve General Quadratic Equation

You should put the function into Standard Form. Solving for x when f(x)=0 will then be a simple process, giving the x-axis intercepts. Your function will have a minimum, because a%3E0.

Answer by gateau052706(3) About Me  (Show Source):
You can put this solution on YOUR website!
The parabola will open upwards because the equation starts positive versus negative. You then have to use the quadratic formula to solve.
To find vertex take (-b/2a, f(-b/2a)):
3/2*2 give you 3/4 or .75
plug that in for f(x).......f(.75)=2(.75)^2-3(.75)+5=3.875
So your vertex is (.75,3.875)
Stick a 0 in for x to find out y-int.....2(0)^2-3(0)+5. y-int = (0,5)
for x-int, you will need to factor. You get (x+1) and (2x-5), so x= -1 and 5/2 or 2.5 (-1,0) and (2.5,0) are your x-ints.
Since a>0 it will be decreasing (-inf.,.75] and increasing [.75,inf.)
AOS is x=.75, make sure you write the x= part, if not it will be wrong.
Hope this helps.