document.write( "Question 1056864: Find the x-intercepts of the parabola with vertex of (-4,2) and y-intercept (0,-30). \n" ); document.write( "

Algebra.Com's Answer #671933 by josmiceli(19441) $\"\"$ $\"About$

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Let the form of the parabola =
\n" ); document.write( " $\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( "The formula for the x-value of the vertex is:
\n" ); document.write( " $\"+x%5Bv%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( "The vertex is at: ( -4, 2 )
\n" ); document.write( " $\"+-4+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+4+=+b%2F%282a%29+\"$
\n" ); document.write( " $\"+b+=+8a+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "The parabola goes through ( 0, -30 )
\n" ); document.write( " $\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( " $\"+-30+=+a%2A0%5E2+%2B+b%2A0+%2B+c+\"$
\n" ); document.write( " $\"+c+=+-30+\"$
\n" ); document.write( "----------------------------------
\n" ); document.write( " $\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( " $\"+y+=+a%2Ax%5E2+%2B+8a%2Ax+-+30+\"$
\n" ); document.write( "Find $\"+a+\"$ using ( -4, 2 ) the vertex
\n" ); document.write( " $\"+2+=+a%2A%28-4%29%5E2+%2B+8a%2A%28-4%29+-+30+\"$
\n" ); document.write( " $\"+32+=+16a+-+32a+\"$
\n" ); document.write( " $\"+-16a+=+32+\"$
\n" ); document.write( " $\"+a+=+-2+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+b+=+8a+\"$
\n" ); document.write( " $\"+b+=+-16+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "The equation is:
\n" ); document.write( " $\"+y+=+-2x%5E2+-+16x+-+30+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "Does it go through ( -4,2 ) ?
\n" ); document.write( " $\"+2+=+-2%2A%28-4%29%5E2+-+16%2A%28-4%29+-+30+\"$
\n" ); document.write( " $\"+2+=+-2%2A16+%2B+64+-+30+\"$
\n" ); document.write( " $\"+2+=+-32+-30+%2B+64+\"$
\n" ); document.write( " $\"+2+=+-62+%2B+64+\"$
\n" ); document.write( " $\"+2+=+2+\"$
\n" ); document.write( "OK
\n" ); document.write( "Does it go through ( 0,-30 )
\n" ); document.write( "Yes
\n" ); document.write( "-----------------------------
\n" ); document.write( "Find x-intercepts ( roots )
\n" ); document.write( " $\"+-2x%5E2+-+16x+-+30+=+0+\"$
\n" ); document.write( " $\"+x%5E2+%2B+8x+%2B+15+=+0+\"$
\n" ); document.write( " $\"+%28+x+%2B+3+%29%2A%28+x+%2B+5+%29+=+0+\"$
\n" ); document.write( " $\"+x+=+-3+\"$
\n" ); document.write( " $\"+x+=+-5+\"$
\n" ); document.write( "The x-intercepts are:
\n" ); document.write( "( -3, 0 )
\n" ); document.write( "( -5, 0 )
\n" ); document.write( "----------------------
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-8%2C+4%2C+-10%2C+4%2C+-2x%5E2+-+16x+-+30+%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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