document.write( "Question 718182: How many times will the graph of y=5x^2-1 intersect: (a) The x-axis? (b) The y- axis? Thank You! \n" ); document.write( "

Algebra.Com's Answer #440789 by josmiceli(19441) $\"\"$ $\"About$

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It can intersect the y-axis either:
\n" ); document.write( "(a) once
\n" ); document.write( "(b) not at all
\n" ); document.write( "If it intersected more than once, that would violate the
\n" ); document.write( "definition of a function, which needs 1 unique value of
\n" ); document.write( " $\"+y+\"$ for each $\"+x+\"$
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\n" ); document.write( "In this case, set $\"+x+=+0+\"$ to find y-crossing
\n" ); document.write( " $\"+y+=+5x%5E2+-+1+\"$
\n" ); document.write( " $\"+y+=+5%2A0+-+1+\"$
\n" ); document.write( " $\"+y+=+-1+\"$
\n" ); document.write( "so, the y-crossing is at (0,-1)
\n" ); document.write( "-------------------------
\n" ); document.write( "The x-crossing(s) is where $\"+y+=+0+\"$ , and there can be
\n" ); document.write( "(a) none
\n" ); document.write( "(b) one
\n" ); document.write( "(c) two
\n" ); document.write( "for a 2nd degree equation, which is what this is.
\n" ); document.write( "In this case there are 2 x-crossings
\n" ); document.write( " $\"+0+=+5x%5E2+-+1+\"$
\n" ); document.write( " $\"+5x%5E2+=+1+\"$
\n" ); document.write( " $\"+x%5E2+=+1%2F5+\"$
\n" ); document.write( " $\"+x+=+1%2Fsqrt%285%29+\"$
\n" ); document.write( " $\"+x+=+-1%2Fsqrt%285%29+\"$
\n" ); document.write( "------------------ \n" ); document.write( "

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