• Nov 21st 2007, 06:10 PM
plasticfang
I was given this question in math class

Quadratic functions may have two, one or no real zeros, but every cubic function must have at least one real zero. explain.

my problem is that i have a real hard time understanding HOW things work in math, and i can usually settle for just being able to use them.
Anyways, can someone try to explain this to me?

also given points on a graph of function P(x) (3,4) and also (6,0), how would i go about applying the transformation y=(x-6)P(x+3) the part i don't understand here is what to do with (x-6)
• Nov 21st 2007, 06:56 PM
Soroban
Hello, plasticfang!

Quote:

Quadratic functions may have two, one or no real zeros,
but every cubic function must have at least one real zero. Explain.

A zero of a function is where its graph crosses the x-axis (x-intercept).

A quadratic function, $y \:=\:ax^2 + bx + c$, is a parabola.
It can open upward or downward,
. . and can cross the x-axis 0, 1, or 2 times.
Code:

  |                    |                    |   |*            *    |                    |   |                    |                    |   | *          *      |*            *    |   |  *        *      |                    |   |    *    *        | *          *      |*            *   |      *            |  *        *      |   |                    |    *    *        | *          *  -+----------------  -+-------*--------  -+--*---------*--   |                    |                    |    *    *   |                    |                    |      *   |                    |                    |

A cubic function has a range from $-\infty$ to $+\infty$.
Its graph extends from the upper-left to the lower-right,
. . or the lower-left to the upper-right.
In either case, it will cross the x-axis at least once.
Code:

          |           |              *           |           |       ----+--*----------*--           *    *         * |    *      *           |      *  *       *  |        *           |           |       *  |           |

We can, of course, draw the horizontal x-axis anywhere.

• Nov 21st 2007, 08:52 PM
plasticfang
thanks for your help. i actually feel pretty dumb now because that was ridiculously simple.