document.write( "Question 1128688: We are given the following equation: f(x)=x^2+25, and are asked to find the Vertex and the X-intercept(s). \n" ); document.write( "

Algebra.Com's Answer #745165 by josmiceli(19441) $\"\"$ $\"About$

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$\"+f%28x%29+=+x%5E2+%2B+25+\"$
\n" ); document.write( "The x-intercept(s) is where $\"+y=0+\"$ , so
\n" ); document.write( " $\"+x%5E2+%2B+25+=+0+\"$
\n" ); document.write( " $\"+x%5E2+=+-25+\"$
\n" ); document.write( " $\"+x+=+%2Bsqrt%28+-25+%29+\"$
\n" ); document.write( " $\"+x+=+5i+\"$
\n" ); document.write( "and, also,
\n" ); document.write( " $\"+x+=+-5i+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "There are 2 imaginary x-intercepts, and no
\n" ); document.write( "real x-intercepts
\n" ); document.write( "-----------------
\n" ); document.write( "Using the general form:
\n" ); document.write( " $\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( "The x-value of the vertex is at:
\n" ); document.write( " $\"+x%5Bv%5D+=+-b%2F%282a%29+\"$ where
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+0+\"$
\n" ); document.write( " $\"+x%5Bv%5D+=+0%2F%282%2A1%29+\"$
\n" ); document.write( " $\"+x%5Bv%5D+=+0+\"$
\n" ); document.write( "Plug this back into equation:
\n" ); document.write( " $\"+y+=+0%5E2+%2B+25+\"$
\n" ); document.write( "The vertex is at ( 0,25 )
\n" ); document.write( "--------------------------------
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-5%2C+100%2C+x%5E2+%2B+25+%29+\"$
\n" ); document.write( " \n" ); document.write( "

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