document.write( "Question 36331: (1) find the x- intercepts of the graph of f(x) =2x^2-4x-4.\r
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\n" ); document.write( "\n" ); document.write( "(2) find all the vertical asymptotes for g(x) = x^2-4/x+2\r
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\n" ); document.write( "\n" ); document.write( "(3) find $\"%28f%2Ag%29\"$ (x) if f(x) =3x-5 and g(x)x^2+1 \n" ); document.write( "

Algebra.Com's Answer #22260 by Nate(3500) $\"\"$ $\"About$

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(1) find the x- intercepts of the graph of f(x) =2x^2-4x-4.
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"2x%5E2%2B-4x%2B-4+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-4%29%5E2-4%2A2%2A-4=48\"$ .
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\n" ); document.write( " Discriminant d=48 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--4%2B-sqrt%28+48+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+48+%29%29%2F2%5C2+=+2.73205080756888\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-4%29-sqrt%28+48+%29%29%2F2%5C2+=+-0.732050807568877\"$
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\n" ); document.write( " Quadratic expression $\"2x%5E2%2B-4x%2B-4\"$ can be factored:
\n" ); document.write( " $\"2x%5E2%2B-4x%2B-4+=+2%28x-2.73205080756888%29%2A%28x--0.732050807568877%29\"$
\n" ); document.write( " Again, the answer is: 2.73205080756888, -0.732050807568877.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-4%2Ax%2B-4+%29\"$

\n" ); document.write( "\n" ); document.write( "(2) find all the vertical asymptotes for g(x)=(x^2-4)/(x+2)
\n" ); document.write( " $\"g%28x%29=%28x%5E2-4%29%2F%28x%2B2%29\"$
\n" ); document.write( " $\"g%28x%29=%28%28x-2%29%28x%2B2%29%29%2F%28x%2B2%29\"$
\n" ); document.write( " $\"g%28x%29=%28x-2%29\"$ where the vertical asymptote is the deleted denominator $\"x%2B2\"$
\n" ); document.write( "so $\"x%2B2\"$ is also expressed as: $\"x=-2%29\"$ that is the vertical asymptote
\n" ); document.write( "In the line below, the point as (-2,-4) doesn't exist....
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Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation $\"-1+x+%2B+1+y+=+-2\"$ describes a sloping line. For any
\n" ); document.write( " equation ax+by+c = 0, slope is $\"-a%2Fb+=+--1%2F1\"$ .

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.

$\"graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+-2-8%2C+-2%2B8%2C+1%2Ax%2B-2+%29+\"$ \n" ); document.write( "

\n" ); document.write( "\n" ); document.write( "(3) find $\"%28f+of+g%29\"$ (x) if f(x) =3x-5 and g(x)x^2+1
\n" ); document.write( "Just plug in g(x) as 'x' for f(x)....
\n" ); document.write( " $\"f%28x%29=3x-5\"$
\n" ); document.write( " $\"f%28x%29=3%28x%5E2%2B1%29-5\"$
\n" ); document.write( " $\"%28f+of+g%29%28x%29=3x%5E2-2\"$ \n" ); document.write( "

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