Sketch the graph of the polynomial function $$ p(x) = -\cancel{\frac{1}{30}x}-4x-3x+5x+ \cancel{x}+2 $$

Tap the blue points to see coordinates.

STEP 1:Find the x-intercepts

To find the x-intercepts solve, the equation $ \color{blue}{ -\cancel{\frac{1}{30}x}-4x-3x+5x+ \cancel{x}+2 = 0 } $

The solution of this equation is:

$$ \begin{matrix}x = \dfrac{ 60 }{ 31 } \end{matrix} $$

(you can use the step-by-step polynomial equation solver to see a detailed explanation of how to solve the equation)

STEP 2:Find the y-intercepts

To find the y-intercepts, substitute $ x = 0 $ into $ \color{blue}{ p(x) = -\cancel{\frac{1}{30}x}-4x-3x+5x+ \cancel{x}+2 } $, so:

$$ \text{Y inercept} = p(0) = 2 $$

STEP 3:Find the end behavior

The end behavior of a polynomial is the same as the end behavior of a leading term.

$$ \lim_{x \to -\infty} \left( -\cancel{\frac{1}{30}x}-4x-3x+5x+ \cancel{x}+2 \right) = \lim_{x \to -\infty} -\frac{1}{30}x = \color{blue}{ \infty } $$

The graph starts in the upper-left corner.

$$ \lim_{x \to \infty} \left( -\cancel{\frac{1}{30}x}-4x-3x+5x+ \cancel{x}+2 \right) = \lim_{x \to \infty} -\frac{1}{30}x = \color{blue}{ -\infty } $$

The graph ends in the lower-right corner.

Graphing Polynomials