Hyperbolas and Cubed Equations?

Question

Okay, well, I have a couple questions in one, so please answer and I'll be VERY happy! thank you

1) Is an equation with cubed in it at anytime a hyperbola? I mean, will you get a hyperbola with a function with 'cubed' in it?

2) How do solve an equation with cubed in it? For example, 2^3 + 4 = 12. i know its easy, but how do u properly solve it?

3) x^2/a^2 - y^2/b^2...the hyperbola function..HOW DO YOU DO IT!!!! lol

4) How do you get a parabola that is facing left or right, not up or down?

Answer 1

1) Is an equation with cubed in it at anytime a hyperbola? I mean, will you get a hyperbola with a function with 'cubed' in it?

A hyperbola is a second order equation. So it will NEVER have a cubed term in it.

2) How do solve an equation with cubed in it? For example, 2^3 + 4 = 12. i know its easy, but how do u properly solve it?

2³ + 4 = 8 + 4 = 12

3) x^2/a^2 - y^2/b^2...the hyperbola function..HOW DO YOU DO IT!!!! lol

The equation of a hyperbola in standard form with center (h,k) is:

(x - h)²/a² - (y - k)²/b² = 1
or
(y - k)²/a² - (x - h)²/b² = 1

4) How do you get a parabola that is facing left or right, not up or down?

Under question 3) the first hyperbola opens left and right, and the second hyperbola opens up and down. You can tell which way they open by noticing which variable, x² or y², has a positive coefficieint and which has negative a negative coefficient.

Answer 2

1) Is an equation with cubed in it at anytime a hyperbola? I mean, will you get a hyperbola with a function with 'cubed' in it?

cubed => max & min OR lattice pt NOT hyperbola

2) How do solve an equation with cubed in it? For example, 2^3 + 4 = 12. i know its easy, but how do u properly solve it?

2^3 + 4 = 12.
=> 2x^3 = 8
=> x = 2
easy
equation with cubed in it => usually solved trail & error
i.e. is +/-1 a solution, or +/-2 a solution,etc