Question

How do you graph `f(x)= (2x^2+5x-12)/(x+4)`?

Answer 1

Factor the numerator using the `a*c` method. Cancel common terms in the numerator and denominator. Make a table of `x` and `y` values. Plot the points, and draw a straight line through the points.

Explanation:

Substitute `y` for `f(x)`.

`y=(2x^2+5x-12)/(x+4)`

Factor the numerator using the `a*c` method.

`2x^2+5x-12`

`ax^2+bx+c`

`a=2;` `b=5;` `c=-12`

`a*c=2*-12=-24`

Find two numbers that when multiplied equal `-24` and when added equal `5`.

The numbers `-3` and `8` fit the criteria.

Rewrite `5x` as `-3x` and `8x`.

`2x^2-3x+8x-12`

Group and factor.

`(2x^2-3x)+(8x-12)` =

`x(2x-3)+4(2x-3)` =

`(x+4)(2x-3)`

Rewrite the numerator as `(x+4)(2x-3)`.

`y=((x+4)(2x-3))/(x+4)`

Cancel `(x+4)`.

`y=(cancel(x+4)(2x-3))/cancel(x+4)` =

`y=2x-3`

Make a table of `x` and `y`. Plot the points, and draw a line through the points.

Table of `x` and `y` values.
`x=-2;` `y=-7`
`x=0;` `y=-3`
`x=2;` `y=1`

graph{y=2x-3 [-11.3, 11.2, -7.56, 3.69]}