Question 535785: y=-2x^2+6 How do I graph this?
Found 2 solutions by lmeeks54, lwsshak3:
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! Two ways, compute some points by hand and plot them on graph paper, or use a spreadsheet or other math software to compute y values from a series of x values that you put in as givens. You decide what x values to use; the y values result from the function described by the equation.
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This equation plots as a parabola that is open at the bottom (like an umbrella). The highest point (maxima) is the coordinate, (0, 6), which is also the y intercept.
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To satisfy myself what it would look like, I plotted points from x = -5 to x = 5, at .5 intervals (the smaller the intervals, the smoother the curve when plotted by Excel). Here are the values I computed and plotted:
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x y
-5.0 -44.0
-4.5 -34.5
-4.0 -26.0
-3.5 -18.5
-3.0 -12.0
-2.5 -6.5
-2.0 -2.0
-1.5 1.5
-1.0 4.0
-0.5 5.5
0.0 6.0
0.5 5.5
1.0 4.0
1.5 1.5
2.0 -2.0
2.5 -6.5
3.0 -12.0
3.5 -18.5
4.0 -26.0
4.5 -34.5
5.0 -44.0
...
Hope this helps,
Lee
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! y=-2x^2+6 How do I graph this?
This is an equation of the standard form for a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
vertex:(0,6)
negative lead coefficient means parabola opens downwards
y-intercept
set x=0
y=6
..
x-intercepts:
set y=0
2x^2=6
x^2=3
x=±√3
..
you now have the vertex(0,6), y-intercept(0,6) and two x-intercepts(±√3,0)
with which you can easily draw the graph of given function.
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