document.write( "Question 703939: Find the equation of the parabola with vertex (4,-4), the parabola opens upwards and is congruent to y=1/2x^2.\r
\n" ); document.write( "\n" ); document.write( "Can you please help me? Thanks so much in advance:) \n" ); document.write( "
Algebra.Com's Answer #433798 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
I don't think you mean congruent because the means they are equal. I think you means same \"shape\" but shift the vertex from (0,0) to (4.-4).
\n" ); document.write( "Given
\n" ); document.write( "(1) y = 1/2*x^2 whose vertex is at (0,0).
\n" ); document.write( "To shift (1) down by 4 units, subtract 4 from (1) and get
\n" ); document.write( "(2) y = 1/2*x^2 - 4
\n" ); document.write( "To shift (2) to the right by 4 units subtract (not add) 4 units from x in (2) and get
\n" ); document.write( "(3) y = 1/2*(x-4)^2 - 4
\n" ); document.write( "Now FOIL (x-4)^2 and (3) becomes
\n" ); document.write( "(4) y = 1/2*(x^2 - 8*x +16) -4 or
\n" ); document.write( "(5) y = 1/2*x^2 - 4*x +8 -4 or
\n" ); document.write( "(6) y = 1/2*x^2 - 4*x + 4
\n" ); document.write( "Let's check this to see if the point (4,-4) is satisfied.
\n" ); document.write( "Is (-4 = 1/2*4^2 - 4*4 + 4)?
\n" ); document.write( "Is (-4 = 8 - 16 + 4)?
\n" ); document.write( "Is (-4 = -8 + 4}?
\n" ); document.write( "Is (-4 = -4)? Yes
\n" ); document.write( "Answer: The equation of the parabola that has its vertex at (4.-4) and opens upward with a compression factor of 1/2 is
\n" ); document.write( "y = 1/2*x^2 - 4*x +4.
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