Question

Find me X and y intercepts givin a polynomial function

Answer 1

y-intercept: value of the function when it crosses y-axis (when x=0)

x-intercept: values of x when the function cross the x-axis (when the function is equal to 0)

$f(x)=x^3-4x^2-25x+100$

To fidn y-intercept evaluate the function when x=0 (find f(0)):

$\begin{gathered} f0)=0^3-4(0)^2-25(0)+100 \\ f(0)=0-0-0+100 \\ f(0)=100 \end{gathered}$

y-intercept: 100

To find x-intercepts; equal the function to 0 and solve x:

$x^3-4x^2-25x+100=0$

Factor by parts:

$\begin{gathered} (x^3-4x^2)+(-25x+100)=0 \\ \\ x^2(x-4)-25(x-4)=0 \\ \\ (x^2-25)(x-4)=0 \end{gathered}$

Solve x: When the product is 0, equal each factor to 0 and solve separately:

$\begin{gathered} x^2-25=0 \\ x^2=25 \\ x=\sqrt[]{25} \\ x=\pm5 \\ \\ \\ x-4=0 \\ x=4 \end{gathered}$

x-intercepts: -5,4,5