Sketch the graph of the polynomial function $$ p(t) = -\frac{42}{100}t-\frac{5}{2}t-\frac{5}{2}+23 $$

Tap the blue points to see coordinates.

STEP 1:Find the x-intercepts

To find the x-intercepts solve, the equation $ \color{blue}{ -\frac{42}{100}t-\frac{5}{2}t-\frac{5}{2}+23 = 0 } $

The solution of this equation is:

$$ \begin{matrix}t = \dfrac{ 1025 }{ 146 } \end{matrix} $$

(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 $ t = 0 $ into $ \color{blue}{ p(t) = -\frac{42}{100}t-\frac{5}{2}t-\frac{5}{2}+23 } $, so:

$$ \text{Y inercept} = p(0) = \frac{ 41 }{ 2 } $$

STEP 3:Find the end behavior

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

$$ \lim_{x \to -\infty} \left( -\frac{42}{100}t-\frac{5}{2}t-\frac{5}{2}+23 \right) = \lim_{x \to -\infty} -\frac{42}{100}t = \color{blue}{ \infty } $$

The graph starts in the upper-left corner.

$$ \lim_{x \to \infty} \left( -\frac{42}{100}t-\frac{5}{2}t-\frac{5}{2}+23 \right) = \lim_{x \to \infty} -\frac{42}{100}t = \color{blue}{ -\infty } $$

The graph ends in the lower-right corner.

Graphing Polynomials