A few days ago
Anonymous

Graph the following parabola: y=(x-7)(x-3)?

Ok, What is up here?!?!? The question read as the title “Graph the following parabola: y=(x-7)(x-3)

I am really confused again . . . I remember I was taught a equation and how to tell if if opens down or up, but I forgot. Can anyone help me out here and shed some light on this? Now I don’t expect a graphed parabola but can you just tell me how I can find the points and actually set it up?

Top 5 Answers
A few days ago
Twiggy

Favorite Answer

The first problem is that you are not given the values of x for which you have to plot the graph for, so let`s look at that first. If you make y = 0, then [x-7][x-3] = 0, so x = 7 or x = 3. This tells you that the graph will cross the x-axis when x is 7 and also when x is 3. So it would be sensible to plot the graph for x from 2 to 8. You now need to construct the table of values for the values of y when x takes the values 2,3,4,5,6,7 and 8. Now when you expand the brackets you get

y = x^2 – 10x + 21. So the table of values looks like this:

x………………y

2……………..5

3……………..0

4…………….. -3

I`m sure you can complete it ! ! !

Now complete the table, and using appropriate scales,

usually 2cm to represent one unit on each axis, you can plot

the graph. Hope this helps, Twiggy.

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A few days ago
Expat Mike
It’s late, so don’t expect brilliance, but here goes:

First, to find where it hits on the x-axis you to set y to 0 (zero). The only way y can equal zero is if one of the sets in the parentheses equals zero. So by this, you can gather that y is zero when x=7 (7-7=0) or when x=3 (3-3=0).

Now you have your points on the x-axis. To see if it opens up or down, you merely need to figure out where it hits the y-axis. At the y-axis, x is zero, right? so y = (0-7)(0-3) or -21. Since the two points of the curve hit the x-axis at 3 and 7, both to right of the y-axis, you know that this is outside those two points, and thus not part of the bell, but part of the extension, and thus it opens down.

That should do it. If any part of that was unfathomable gibberish, I apologize. I need to go to bed.

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A few days ago
krysteven
ok, if the expanded equation is negative (the x^2 has a negative sign in front of it it opens downward). The factored version you have there shows the two places the graph crosses the x axis, so it crosses at 7 and 3. The equation you are thinking of is the quadratic formula maybe, but that only helps you find the x intercepts anyway so in this case you don’t need it. That is only necessary when you cannot factor the polynomial.
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A few days ago
Anonymous
combine the parentheses and punch it in a graphing calculator 🙂
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A few days ago
Anonymous
make it a sum of a perfect square and some constant…….

………..then using shifting of origin and intercept method plot its graph

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