Question

Create your own quadratic equation and demonstrate how it would be solved by graphing, factoring, the quadratic formula, and by completing the square. (5 points)

Answer 1

Here's a good equation of a quadratic that factors nicely and can be graphed with use of completing the square. That completing the square gives the general form (vertex form) and is really good for giving the maximum or minimum point. It also gives the axis of symmetry. First off, here's a graph of:\[y = x ^{2} - 10x + 21\]to look at before we solve it for the zeros (x-intercepts -> places where the graph crosses the x-axis, which is where y=0) and for the min/max. In our case, it will be a min.

Answer 2

Ok wait one sec please

Answer 3

ok continue please

Answer 4

This is a computer-generated graph from "fooplot.com". But if we were to have done this by hand, we would have needed to find where it crossed the x-axis. We can see that this is at x = 3 and x = 7. But to know this, we have to set the initial equation to "0" and solve:

x^2 - 10x + 21 = 0 -> factoring we get:

(x - 7)(x - 3) = 0

So, we know that at either x = 7 or 3 either the first or second factor will be "0" and the graph will hit the x-axis (y=0) at either of those 2 values of "x". Those are the x-intercepts. To get the y-intercept, we plug x=0 into the original equation and get:

y = (0)^2 - 10(0) + 21 = 21

And we can see that on the graph. As for getting the minimum value:

y = x^2 - 10x + 21 -> y = (x - 10x + 25) + 21 - 25

y = (x - 5)^2 - 4

So, at x = 5, that first term is 0 and the whole right side has a minimum of -4

That's at (5, -4)

Answer 5

Is this all I need.

Answer 6

We still have to do the quadratic formula. From the other posts, you have the quadratic formula and you can identify:

a = 1, b = -10, and c = 21

Solving that, you'll come up with x = 7 and 3, just like we got when factoring.

One more thing about the graph. The axis of symmetry is the vertical line:

x = 5

so you can see that at x = 10 we also have y = 21. That's from 5-5 = 0 and 5+5 = 10

Answer 7

Ok thank you again. I really like you more than the other guy because he just looked at my question and left.

Answer 8

Well, sometimes some helpers can do some problems better than other problems. I happen to do quadratics well, so I don't mind them. You might want to go over this problem at least 4-5 times because there is a LOT to learn from this one and everything we've done is contained in this one problem.

Answer 9

ok! Now, I can go eat!

Answer 10

Thank you some much I am sorry to keep you waiting so long. Bye and wish you good food :)

Answer 11

Thanks very much!

Answer 12

again bye.

Answer 13

u2, and have a reat night! @magbak

Answer 14

great