document.write( "Question 62480: For f of x, f(x)=3(x-4)squared - 1 find the coordinates of the vertex, the equation of the axis of symmetry, the x-intercepts(if any) and the y-intercept. \n" ); document.write( "

Algebra.Com's Answer #43368 by 303795(602) $\"\"$ $\"About$

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$\"f%28x%29=3%28x-4%29%5E2-1\"$ \r
\n" ); document.write( "\n" ); document.write( "The axis of symmetry is at x=4 because x=4 makes the part in the bracket = 0.
\n" ); document.write( "The vertex is on the axis of symmetry so it will be at -1. Can either just look at the -1 at the end of the equation or substitute x=4 into the equation.\r
\n" ); document.write( "\n" ); document.write( "The y intercept occurs when x=0 so substitute x=0 into the equation.
\n" ); document.write( " $\"f%28x%29=3%280-4%29%5E2-1\"$
\n" ); document.write( " $\"f%28x%29=3%2A16-1\"$
\n" ); document.write( " $\"f%28x%29=48-1\"$
\n" ); document.write( " $\"f%28x%29=47\"$ \r
\n" ); document.write( "\n" ); document.write( "The x intercepts occur when f(x)=0 so substitute that into the equation.
\n" ); document.write( " $\"0=3%28x-4%29%5E2-1\"$ Add 1 to each side of the equation
\n" ); document.write( " $\"0%2B1=3%28x-4%29%5E2-1%2B1\"$
\n" ); document.write( " $\"1=3%28x-4%29%5E2\"$ Divide each side by 3
\n" ); document.write( " $\"1%2F3=3%28x-4%29%5E2%2F3\"$
\n" ); document.write( " $\"1%2F3=%28x-4%29%5E2\"$ Find the square root of each side
\n" ); document.write( " $\"1%2Fsqrt%283%29=x-4\"$ or $\"-%281%2Fsqrt%283%29%29=x-4\"$ Solve for x by adding 4 to each side of the equation
\n" ); document.write( " $\"x+=+4+%2B+1%2Fsqrt%283%29\"$ or $\"x=4-%281%2Fsqrt%283%29%29\"$ \r
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