Question 485722: Hi, I needed help with my precalc honors summer work, and I was wondering if someone could help me. How do I:
a) Express the quadratic equation in standard form
b) Sketch the graph (I know how do do this)
c) Find its maximum or minimum value (What does this mean? The vertex?)
What I have so far:
Original equation: f(x)=2x-x^2
A)
f(x)=2x-x^2
-x^2+2x+0
(-x^2+2x+1)-1
-(x^2-2x-1)+1
I got stuck...I would love it if someone would explain to me how to get rid of the negative coefficient so I can factor it, and how to put this equation into standard form. Also I would appreciate it a ton if someone could tell me what minimum/maximum of a graph is and how to find it. Thanks a ton, Jess
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! a) Express the quadratic equation in standard form
b) Sketch the graph (I know how do do this)
c) Find its maximum or minimum value (What does this mean? The vertex?)
What I have so far:
Original equation: f(x)=2x-x^2
**
a) Quadratic equations are parabolas of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
y=-x^2+2x
completing the square
y=-(x^2-2x+1)+1
y=-(x-1)^2+1
vertex: (1,1)
The negative sign of the lead coefficient means that the parabola opens downwards, that is, it has a maximum value=1 (y-coordinate of vertex)
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see graph below as a visual check on the answers:
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