Question

Find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph of the function. f(x)=x+3x^2−25 Enter the intercepts as points, (a,b) .

Answer 1

Given:

f(x)= x + 3x^2 - 25

Rewrite:

f(x)= 3x^2 + x - 25

a= 3

b= 1

c= -25

Apply the Quadratic formula:

$\frac{-b\pm\sqrt[\placeholder{⬚}]{b^2-4ac}}{2a}$

Replacing:

$\frac{-1\pm\sqrt[\placeholder{⬚}]{1^2-4(3)(-25)}}{2(3)}$$\frac{-1\pm\sqrt[\placeholder{⬚}]{301}}{6}$

positive:

-1+√301 / 6 = 2.72

negative

-1-√301 / 6 = -3.06

Intercepts ( 2.72 , 0 ) (-3.06,0)

There are no asymptotes because it is not a rational function

Graph: