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

Jul 1, 2015

Factor the numerator using the $a \cdot c$ 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 $f \left(x\right)$.

$y = \frac{2 {x}^{2} + 5 x - 12}{x + 4}$

Factor the numerator using the $a \cdot c$ method.

$2 {x}^{2} + 5 x - 12$

$a {x}^{2} + b x + c$

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

$a \cdot c = 2 \cdot - 12 = - 24$

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

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

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

$2 {x}^{2} - 3 x + 8 x - 12$

Group and factor.

$\left(2 {x}^{2} - 3 x\right) + \left(8 x - 12\right)$ =

$x \left(2 x - 3\right) + 4 \left(2 x - 3\right)$ =

$\left(x + 4\right) \left(2 x - 3\right)$

Rewrite the numerator as $\left(x + 4\right) \left(2 x - 3\right)$.

$y = \frac{\left(x + 4\right) \left(2 x - 3\right)}{x + 4}$

Cancel $\left(x + 4\right)$.

$y = \frac{\cancel{x + 4} \left(2 x - 3\right)}{\cancel{x + 4}}$ =

$y = 2 x - 3$

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]}