Use the given information to create the equation for the rational function.

Question

Use the given information to create the equation for the rational function. The function is written in factored form to help you see how the given information shapes our equation. If the leading coefficient is not an integer enter the value as a fraction.

Vertical asymptote at x=-1, double zero at x=2, y-intercept at (0,2).

Answer 1

y = 3(x-2)^2/2(x+1)

or

y = 3(x-2)^2/(2x+2) lots of twos, 4 of them

or

y = f(x) = (3x^2-12x+12)/(2x+2)

asymptote x=-1 is given by the denominator = 0 when x=-1

a zero is when x=2, the point (2,0) which is not technically an x intercept as the curve doesn't intersect but is tangent to the x axis, just touching, but not crossing

when x=2, y=0 is the point (0,2), the y intercept, where the curve intersects the y axis

y(x) =y(0) = (0-2)^2/(2(0)+2) = 4/

a double zero means put an exponent of 2 over the factor (x-2): (x-2)^2