1. Some more general questions..

Hey,

I have some general questions from "all-around" math:

• When factoring, why do you have to use perfect squares?
• Is the equation ax^2+bx+c=0 the same as the equation y=ax^2+bx+c? (referring to quadratics)
• What does the term "difference of squares" imply?
• Are there any general rules when factoring trinomials?

Thanks everyone.
-NineZeroFive

2. This,
$\displaystyle ax^2+bx+c=0$ is an equation. Meaning it has to be solved.

This,
$\displaystyle ax^2+bx+c=y$ is a function. It represents the relationship between the x-coordinate and y-coordinate.
---
Diffrence of square means,
$\displaystyle x^2-y^2$ and they can always be factored.
$\displaystyle (x+y)(x-y)$
---
Why use perfect squares?
You mean why bring everything to perfect square in a conic? Because after you used perfect squares the shape of the conic is easily recognizable. And also it can be graphed easily by simply doing a translation of the axes.

3. Originally Posted by ThePerfectHacker
This,
$\displaystyle ax^2+bx+c=0$ is an equation. Meaning it has to be solved.

This,
$\displaystyle ax^2+bx+c=y$ is a function. It represents the relationship between the x-coordinate and y-coordinate.
---
Diffrence of square means,
$\displaystyle x^2-y^2$ and they can always be factored.
$\displaystyle (x+y)(x-y)$
---
Why use perfect squares?
You mean why bring everything to perfect square in a conic? Because after you used perfect squares the shape of the conic is easily recognizable. And also it can be graphed easily by simply doing a translation of the axes.

I mean..why must we use perfect squares when factoring? :S

4. Also, what is the x intercept(s) and y intercept of $\displaystyle y=x^2$? I'm pretty sure I have the correct answer, just want to confirm because the answer on the back of the textbook I'm using seems 'wierd'. It says the x-intercept is 12 (??) and y inctercept is 0 (which I understand).

Can someone please use the Quadractic formula to figure out the x-intercept(s) of the above equation, if there are any?

Thanks again,
-NineZeroFive

5. The x-intercept would be where the graph crosses/touches the x-axis. Thus at this point y=0. So this occurs when 0=x^2, obviously at 0.

The y-intercept would be where the graph crosses/touches the y-axis. Thus at this point x=0. So this occurs when y=0^2, or 0.

6. Originally Posted by Jameson
The x-intercept would be where the graph crosses/touches the x-axis. Thus at this point y=0. So this occurs when 0=x^2, obviously at 0.

The y-intercept would be where the graph crosses/touches the y-axis. Thus at this point x=0. So this occurs when y=0^2, or 0.
Thats, what I thought, Thanks, I guess I'll have to ask the teacher tomorrow.

Three more questions: (both referring to parabolas)

If an expression is in the form of $\displaystyle ax^2+bx+c$, and the question asks you to find the y-intercept, how would you do so?

Also, when using the Quadratic formula, how to you know when there is only 1 x-intercept instead of the usual 2?

Can someone please use the Quadractic formula to figure out the x-intercept(s) of the equation $\displaystyle y=x^2$, if there are any?

Thanks alot.
-NineZeroFive

7. Originally Posted by NineZeroFive
Thats, what I thought, Thanks, I guess I'll have to ask the teacher tomorrow.

Three more questions: (both referring to parabolas)

If an expression is in the form of $\displaystyle ax^2+bx+c$, and the question asks you to find the y-intercept, how would you do so?
solve for x=0
Also, when using the Quadratic formula, how to you know when there is only 1 x-intercept instead of the usual 2?
there is a thing called the discriminant $\displaystyle b^2-4ac$ (it is the thing under the radical in the quadratic formula) if the discriminant is negative there is no x-intercept, if positive there are 2 x-intercepts, and if it equals 0 than there is 1 x-intercept.

$\displaystyle x=\frac{\neg b\pm\sqrt{\bold{b^2-4ac}}}{2a}$
(the discriminant is bold)
Can someone please use the Quadractic formula to figure out the x-intercept(s) of the equation $\displaystyle y=x^2$, if there are any?

Thanks alot.
-NineZeroFive
write out the equation in full...
$\displaystyle y=ax^2+bx+c\quad\Rightarrow\quad 0=1x^2+0x+0$

than solve...

$\displaystyle x=\frac{\neg b\pm\sqrt{b^2-4ac}}{2a}$

$\displaystyle x=\frac{\neg 0\pm\sqrt{0^2-4(1)(0)}}{2(1)}$

$\displaystyle x=\frac{\pm\sqrt{0}}{2}$ the discriminant is 0, therefore we know there is only 1 solution.

~ $\displaystyle Q\!u\!i\!c\!k$

8. Originally Posted by Quick
solve for x=0
there is a thing called the discriminant $\displaystyle b^2-4ac$ (it is the thing under the radical in the quadratic formula) if the discriminant is negative there is no x-intercept, if positive there are 2 x-intercepts, and if it equals 0 than there is 1 x-intercept.

$\displaystyle x=\frac{\neg b\pm\sqrt{\bold{b^2-4ac}}}{2a}$
(the discriminant is bold)

write out the equation in full...
$\displaystyle y=ax^2+bx+c\quad\Rightarrow\quad 0=1x^2+0x+0$

than solve...

$\displaystyle x=\frac{\neg b\pm\sqrt{b^2-4ac}}{2a}$

$\displaystyle x=\frac{\neg 0\pm\sqrt{0^2-4(1)(0)}}{2(1)}$

$\displaystyle x=\frac{\pm\sqrt{0}}{2}$ the discriminant is 0, therefore we know there is only 1 solution.

~ $\displaystyle Q\!u\!i\!c\!k$

Thanks ALOT Quick. YOU ARE AMAZING!!

BTW: Your PM inbox is full.

9. Originally Posted by NineZeroFive
Three more questions: (both referring to parabolas)
This is one of the funniest mistakes in grammar I've ever seen.

Also, I wanted to say that when factoring you don't need to make things into perfect squares, it's just a convenient thing to do.

10. Originally Posted by NineZeroFive
Hey,

I have some general questions from "all-around" math:

• Are there any general rules when factoring trinomials?

Thanks everyone.
-NineZeroFive

when given an expression in the form $\displaystyle x^2+bx+c$ the factors will be in the form $\displaystyle (x+d)(x+g)$

when given an expression in the form $\displaystyle x^2-bx+c$ the factors will be in the form $\displaystyle (x-d)(x-g)$

when given an expression in the form $\displaystyle x^2+bx-c$ the factors will be in the form $\displaystyle (x+d)(x-g)$ where $\displaystyle d>g$

when given an expression in the form $\displaystyle x^2-bx-c$ the factors will be in the form $\displaystyle (x+d)(x-g)$ where $\displaystyle d<g$