document.write( "Question 150468: write the equation of the parabola with the same shape as f(x)=-2x^2 but with the vertex (-3,2). \n" ); document.write( "

Algebra.Com's Answer #110434 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Go back to the general formula for a parabola which is
\n" ); document.write( " $\"y+=+ax%5E2+%2B+bx+%2B+c\"$
\n" ); document.write( "The formula for the x-coordinate of the vertex is $\"%28-b%29+%2F+%282a%29\"$
\n" ); document.write( "With the parabola $\"y+=+-2x%5E2\"$ ,
\n" ); document.write( " $\"a+=+-2\"$
\n" ); document.write( " $\"b+=+0\"$
\n" ); document.write( " $\"c+=+0\"$
\n" ); document.write( "So, $\"x+=+0+%2F+2%2A%28-2%29+=+0\"$
\n" ); document.write( "and
\n" ); document.write( " $\"y+=+-2%2A%280%29%5E2\"$
\n" ); document.write( " $\"y+=+0\"$
\n" ); document.write( "So, the vertex of this parabola is (0,0). You are asked to keep the
\n" ); document.write( "shape the same, but move the vertex to (-3,2)
\n" ); document.write( "I can say $\"%28-b%29+%2F+%282a%29+=+-3\"$
\n" ); document.write( "I don't want $\"a\"$ to change, because that would change the shape, so
\n" ); document.write( " $\"a+=+-2\"$
\n" ); document.write( " $\"%28-b%29+%2F+2%2A%28-2%29+=+-3\"$
\n" ); document.write( " $\"-b+=+12\"$
\n" ); document.write( " $\"b+=+-12\"$
\n" ); document.write( "So far, I have $\"y+=+-2x%5E2+-+12x+%2B+c\"$
\n" ); document.write( "I can use (-3,2) to find $\"c\"$
\n" ); document.write( " $\"2+=+-2%2A%28-3%29%5E2+-+12%2A%28-3%29+%2B+c\"$
\n" ); document.write( " $\"2+=+-18+%2B+36+%2B+c\"$
\n" ); document.write( " $\"c+=+2+%2B+18+-+36\"$
\n" ); document.write( " $\"c+=+-16\"$
\n" ); document.write( " $\"y+=+-2x%5E2+-+12x+-+16\"$ answer
\n" ); document.write( "I'll plot both these equations
\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%5E2%2C+-2x%5E2+-+12x+-+16%29+\"$
\n" ); document.write( " Each vertex looks OK \n" ); document.write( "

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