SOLUTION: (1) find the x- intercepts of the graph of f(x) =2x^2-4x-4. (2) find all the vertical asymptotes for g(x) = x^2-4/x+2 (3) find {{{(f*g)}}}(x) if f(x) =3x-5 and g

Question 36331: (1) find the x- intercepts of the graph of f(x) =2x^2-4x-4.

(2) find all the vertical asymptotes for g(x) = x^2-4/x+2

(3) find (x) if f(x) =3x-5 and g(x)x^2+1
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
(1) find the x- intercepts of the graph of f(x) =2x^2-4x-4.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=48 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.73205080756888, -0.732050807568877. Here's your graph:

(2) find all the vertical asymptotes for g(x)=(x^2-4)/(x+2)

where the vertical asymptote is the deleted denominator
so is also expressed as: that is the vertical asymptote
In the line below, the point as (-2,-4) doesn't exist....

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .

X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -2/-1 = 2.
Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -2/1 = -2.
Slope is --1/1 = 1.
Equation in slope-intercept form: y=1*x+-2.

(3) find (x) if f(x) =3x-5 and g(x)x^2+1
Just plug in g(x) as 'x' for f(x)....

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