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

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) (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 .
Answer by gateau052706(3) (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.

RELATED QUESTIONS
Given the quadratic function: f(x) = -1/2x^2-3x+5/2 a. Determine whether the parabola (answered by MathLover1)
Given the equation -5(x-2)^2-1=y a. Identify the vertex. b. Identify the axis of... (answered by ewatrrr)
For the given function, (a) determine whether the graph opens upward or downward, (b)... (answered by Fombitz)
Write the equation of the parabola with the shape as f(x)=-2x^2, but with the vertex... (answered by lwsshak3)
For the given function, (a) determine whether the graph opens upward or downward, (b)... (answered by lwsshak3)
For the given function, (a) determine whether the graph opens upward or downward, (b)... (answered by lwsshak3)
Find the vertex of the graph of f(x)= 3x^2-12x+5 and determine whether the graph opens up (answered by stanbon,MathLover1,MathTherapy)
y=x^2+1 I need to find whether the graph opens up, or opens down, find the vertex, and... (answered by MathTherapy)
Tell whether the graph opens up or down write an equation of the axis of symmetry... (answered by nerdybill,Mathtut)