Parabolas, finding the X-intercept and other questions

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Chuck Norris

New member
Joined
Jun 13, 2007
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4
Hello, this is my first post here, hope to use this place more often but i was having this particular problem. After searching to see if anyone had a similar problem I gave up hope, too many posts came up with the search function and I saw some people posted images for the math equations, not sure how to do this but ill try my best how to make it readable.

I have a few problems, which i thought, I knew a formula

quadratic.png


Ive tried it in a few problems, sometimes it works sometimes it doesn't ill give you some examples (no I'm not trying to get you to do my homework for me :p) Also how the heck do you do a square root sign?

2x(2) + x - 2

I came to the conclusion that
-1+(Square Root Sign)17
4

Well, I thought that was right, but then I came to a new one

The x-intercepts are -7.06 and 1.06 so i was given 5 examples on what it could be

A) y=2x(2) +6x -7
B) y= x(2) +3x -4
C) y=2x(2) +6x -8
D) y=2x(2) +12x -15
E) y=2x(2) +x -2

Now, I swear that I have tried them over and over and over again! And they wont work with the formula
quadratic.png


Now, I was wondering if i was looking at it wrong, i go -b +/- (Square Root Sign) b(2) -4ac and then after i get the answer i divide by 2a.

Also, another one we get the equation
x(2) +6x -10
And have to figure out the x-intercepts and y-intercept

And my mother ensures me that its -3-(Square Root Sign)19, -3+(Square Root Sign)19 and -10

I first came up with the answer -6 +/- (Square Root Sign) 36 + 40
2
Is it 4*4 = 16 or 4^4 = 16? Sorry if its 1 way or the either
So my mum suggests that I go (Square Root Sign)19*4 and then that becomes 2(Square Root Sign)19 and well I was wondering, can you really do that? She says it then becomes

-6+/- 2(Square Root Sign)19
2

Divide everything by 2

-3 +/- (Square Root Sign)19

Now it seems to fit the answer, but can you do that with any equation? Because I've been seeing that it may be a reason why my equations wither and die and give the most random incorrect answers.

Ok, well thats about it from me, if anyone has any questions about how some of this didn't make sense (or did it?) just post, ill reply. Any important equations/formula id need for my term test will be gratefully absorbed.

Thanks, anyone that can help, go ahead

Edit: Fixed some underline errors
 
Pretty good first try, Chuck. You managed to get images in!

You can use this thing: ^ to signify an exponent. "x squared" would be x^2. Just use parentheses and spacing liberally to clarify meaning.

Things don't line up unless you force them to do so. It is not a trivial task. Learning just a little LaTeX will be to your great advantage.

To your point, you have the right formula. It is not an inconsistent formula. It works ALL the time. Something else is going wrong.

There is a bit of a trick on these things. The axis of symmetry is at EXACTLY the average of the two x-intercepts. If the x-intercepts are (0,0) and (2,0), the axis of symmetry is x = 1. Very neatly, the asix of symmetry can be seen in the formula, simply x = -b/(2a)

For your example, we see that (-7.06+1.06)/2 = -3.

Now all that is needed is to find a -3 from -b/(2a).

A) -6/4 Nope
B) -3/2 Nope
C) -6/4 Nope
D) -12/4 = -3 Looking Good.
E) -1/4 Nope.

So then, we have a suspect. Had we hit none of them, we would have complained that the problem was a little silly.

With a = 2, b = 12 anc c = -15, out pops x = -7.062019 and x = 1.062019. For greater convenience, one may wish to use exact values: \(\displaystyle \L \frac{\sqrt{66}-6}{2}\) and \(\displaystyle \L -\frac{\sqrt{66}+6}{2}\)
 
Chuck Norris said:
how the heck do you do a square root sign?
Click to expand...
To learn how to use LaTeX formatting or how to use standard web-safe formatting, please review the links in the "Forum Help" pull-down menu at the very top of every forum page. :wink:

Chuck Norris said:
2x(2) + x - 2
Click to expand...
(I will guess that "(2)" means "^2".) Did this quadratic equal zero, or did it equal something else? If zero, then you actually had:

. . . . .2x^2 + x - 2 = 0

Applying the Quadratic Formula, we see that a = 2, b = 1, and c = -2, so:

. . . . .x = ( -(1) +/- sqrt[(1)^2 - 4(2)(-2)] ) / 2(2)

. . . . . . .= ( -1 +/- sqrt[1 - 4(-4)] ) / 4

. . . . . . .= ( -1 +/- sqrt[1 + 16] ) / 4

...and so forth.

Chuck Norris said:
I came to the conclusion that -1+(Square Root Sign)17
4
Click to expand...
I will guess that you mean the following:

. . . . .( -1 +/- sqrt[17] ) / 4

But how did you get this? Without knowing what your steps were, there is little way to help you find any errors. Please reply showing your work, similar to how I did, above.

Also, on what basis did you decide that the above was incorrect?

Chuck Norris said:
The x-intercepts are -7.06 and 1.06 so i was given 5 examples on what it could be

A) y=2x(2) +6x -7
B) y= x(2) +3x -4
C) y=2x(2) +6x -8
D) y=2x(2) +12x -15
E) y=2x(2) +x -2

Now, I swear that I have tried them over and over and over again! And they wont work with [the Quadratic Formula]
Click to expand...
Since the Quadratic Formula will solve any quadratic equation, it would help if you showed what you mean when you say that none of the above is solveable using the Formula.

Chuck Norris said:
x(2) +6x -10
And have to figure out the x-intercepts and y-intercept
Click to expand...
To find x-intercept(s), plug "0" in for "y", and solve.
To find y-intercept(s), plug "0" in for "x", and solve.

Chuck Norris said:
my mother ensures me that its -3-(Square Root Sign)19, -3+(Square Root Sign)19 and -10
Click to expand...
Your mother assures you that which is the three values listed? How did each of you arrive at your answers? What were your steps and reasoning?

Thank you! :D

Eliz.
 
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