Algebra 2 Homework...Help!?

Filed under: enart.cgnq.com — mike @ March 11, 2010 edit

so i tried to ask my teacher about this in class today, but the teacher didn't really answer my question, so i have no idea how to do this....

find the x-intercept(s) of the following:

y = (x - 5)/(3x + 2)

y = (-2x^2)/(x^2 - 9)

y = (x^2 -10x + 24)/(3x)

y = x/(x^2 - 4x -12)

best answer will go to the person who gives a THOROUGH walkthrough

The definition of an x intercept is the point where the line crosses the x axis when y=0, so your first step is to remember y is equal to 0. I think I'm doing this right; I know I'm isolating the x correctly, it's the setting y=0 part I will have to look up when I'm finished.

y = (x - 5)/(3x + 2) Multiply both sides by (3x+2)
y(3x+2)=(x-5) distribute:
3xy+2y=x-5 add 5 to both sides:
3xy+2y+5 =x subtract 3xy from both sides:
2y+5=x-3xy factor out the x
2y+5=x(1-3y) divide by (1-3y)
(2y+5)/(1-3y)=x set y to 0
5=x

y = (-2x^2)/(x^2 - 9) Multiply both sides by (x^2-9)
y(x^2-9)=(-2x^2) distribute
x^2y-9y=2x^2 subtract x^2y from both sides:
-9y=2x^2-x^2y factor out x^2
-9y=x^2(2-y) divide by (2-y)
(-9y)/(2-y)=x^2 take the square root of both sides:
√(-9y)/(2-y)=x, set y to 0
√2=x

y = (x^2 -10x + 24)/(3x) Multiply by 3x to clear the denominator:
3xy=(x^2 -10x + 24) factor
3xy=(x-6)(x-4) Someone has to check this one for me, if I set y=0 now then x=6 and x=4, your graph is a parabola.

y = x/(x^2 - 4x -12)
Rules say clear the denominator, so multiply both sides by the quadratic:

y(x^2 - 4x -12)=x factor the quadratic
y(x+2)(x-6)=x but that makes no sense, and I can't divide by y because y=0, so maybe x=0 too. Sorry, I'm lost on this one. Maybe someone else will come along, or maybe you can print this out and ask your teacher if it's what she's/he's looking for.

wpf :(

The X intercept occurs when Y=0. So, the X-intercept of

Y = (x-5)/(3x+2)

happens where

0 = (x-5)/(3x+2)

And that happens where

0 = x-5

So,

x=5.

The rest are going to be similar.

There's a gotcha: If the denominator is 0 at that point, then you can't use the intercept, because the function is undefined there. So, you have to check:

3x+2
3·5+2
15+2
17

Not 0, so you're OK.

Finding the x-intercept implies that y = 0. The only way to make y = 0 is if the numerator of your polynomial "fractions" equal 0.
So...
1. x-5=0 ==> x=5
2. -2x^2=0 ==> x=0
3. x^2-10x+24 ==> x=6 or x=4
4. x = 0

None of these cause a division by 0 so its all good.

well the x intercept is when the line crosses the x line, so the x number can be any number but y is ALWAYS 0. so to solve for the x intercept, you change y to 0 and solve for x.

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