Question 386561: how do you graph y=3xsquared - 6x + 7
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
the vertex form of a parabola,  where(h,k) is the vertex
graphing
y = 3x^2 - 6x + 7 completing the square to put into vertex form
y = 3(x^2-2x) + 7
y = 3[(x-1)^2 - 1] + 7
y = 3(x-1)^2 -3 + 7
y = 3(x-1)^2 + 4 vertex is Pt (1,4) a = 3 > 0 parabola opens upward
Pt(0,7) Pt(2, 7) on the parabola
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Better than that, I'll tell you how to graph
\ =\ ax^2\ +\ bx\ +\ c)
Then you can do any problem like the one you asked about.
1. Find the  -coordinate of the -intercept. The -coordinate of the -intercept is equal to the value of ) , which is ^2\ +\ b(0)\ +\ c\ =\ c) . Hence, the -intercept is the point ) . Plot the point.
2. Calculate the  -coordinate of the vertex. The -coordinate of the vertex is given by the formula:
3. Calculate the -coordinate of the vertex. The -coordinate of the vertex is the value of the function at the -coordinate of the vertex.
\ =\ \rho\left(\frac{-b}{2a}\right)\ =\ a\left(\frac{-b}{2a}\right)^2\ +\ b\left(\frac{-b}{2a}\right)\ +\ c)
Just plug in the number from step 2 and do the arithmetic. Now that you have the values  and  , create the ordered pair ) . Plot the point.
4. Determine if you have any -intercepts. Calculate the discriminant:
If  , then you have two distinct -intercepts.
If  , then the vertex is actually on the -axis. That is to say, the value you computed for in step 3 should have been zero. (if not, you have an arithmetic error. Check steps 2, 3, AND 4)
If  , then the graph does not intersect the -axis.
5. If your result was , calculate the real number zeros of the function. Set the function equal to zero and solve. You can use factoring, completing the square, or the quadratic formula as is appropriate to your problem. In general, the -coordinates of the intercepts are:
Calculate the two zeros and then create the two ordered pairs, ) and ) . Plot these two points.
6. Find the point symmetrical to the -intercept. By symmetry, a function value equal to the function value at the -intercept is found at a distance from the vertex equal to the distance from the vertex to the -axis and on the other side of the vertex]. The distance from the -axis to the vertex is , so on the other side of the vertex is a point with a function value of  , namely ) . Plot the point.
So far you have either 3 or 5 points plotted depending on the results of step 4. Depending on your desire for precision in your graph, you may want to create a few more points. To do this, select an -value near the vertex that is an integer, determine the function value at this -value, create an ordered pair from the selected -value and the calculated function (-) value. Plot the point. Use symmetry to plot a point equidistant from the vertex on the other side of the vertex. Repeat as often as you like.
7. Final step. Sketch a smooth curve through you plotted points.
John
My calculator said it, I believe it, that settles it
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