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Question 425171: can you help me understan how to graph equations useing the formula y=ax^2+bc+C so that i can do my homework..thank you
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Step 1, find the  -coordinate of the vertex.
Step 2, find the  -coordinate of the vertex.
^2\ +\ b\left(\frac{-b}{2a}\right)\ +\ c)
Step 3, plot the vertex point ) .
Step 4, graph a dashed vertical line through the vertex point. This is the axis of symmetry (Equation of the axis of symmetry  ).
Step 5, find the -coordinate of the -intercept.
^2\ +\ b(0)\ +\ c)
which is to say
Step 6, plot the point ) where  is the -coordinate value you calculated in Step 5
Step 7, determine whether there are zero, 1, or 2 -intercepts.
Calculate the discriminant which is the part of the quadratic formula under the radical, to wit:
If  Then you have two -intercepts.
If  Then you have one -intercept.
If  Then you have zero -intercepts.
Step 8, if there are more than zero -intercepts, use the quadratic formula to find the -coordinate(s) of the -intercept(s).
Step 9, plot the points ) and ) where  and  are the -coordinates you calculated in Step 8.
Step 10, write an ordered pair where the -coordinate is 2 times the value of the -coordinate of the vertex (from Step 1) and the -coordinate is the value of the -coordinate of the -intercept (from Step 5). This point is on the graph because of the properties of symmetry.
At this stage of the process you will have either 3 or 5 points plotted. 3 if you have 0 or 1 -intercepts or 5 if you have 2 -intercepts. You can either draw a smooth curve through your set of points now, or, if it pleases you (or more to the point if it pleases your teacher/instructor/professor/tutor) you can just pick any heretofore unused value of and calculate the resulting value of and repeat the process as often as you like and then draw your smooth curve.
John
My calculator said it, I believe it, that settles it
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