document.write( "Question 539861: I need help finding the X and Y intercepts and vertex of Y=3X^2-6X-5 \n" ); document.write( "

Algebra.Com's Answer #353575 by KMST(5328) $\"\"$ $\"About$

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$\"Y=3X%5E2-6X-5\"$ intercept the y-axis (which is the $\"X=0\"$ line)
\n" ); document.write( "at $\"Y=-5\"$ . So the y-intercept is the point is (0,-5).
\n" ); document.write( "Because $\"3%28X-1%29%5E2-8=3%28x%5E2-2x%2B1%29-8=3X%5E2-6X%2B3-8=3X%5E2-6X-5\"$ ,
\n" ); document.write( "The equation can be re-written as
\n" ); document.write( " $\"Y=3%28X-1%29%5E2-8\"$ ,
\n" ); document.write( "showing that the vertex is the point with $\"X=1\"$ and $\"Y=-8\"$ .
\n" ); document.write( "So the vertex is the point (1,-8).
\n" ); document.write( "The x-intercepts are the points where the parabola crosses the x-axis (which is the $\"Y=0\"$ line).
\n" ); document.write( "At those points, substituting $\"Y=0\"$ in the modified equation, we see that
\n" ); document.write( " $\"0=3%28X-1%29%5E2-8\"$ <--> $\"3%28X-1%29%5E2=8\"$ <--> $\"%28X-1%29%5E2=8%2F3\"$
\n" ); document.write( "That gives us two solutions
\n" ); document.write( " $\"X-1=sqrt%288%2F3%29\"$ and $\"X-1=sqrt%288%2F3%29\"$
\n" ); document.write( "or $\"X=1+%2B-+sqrt%288%2F3%29\"$
\n" ); document.write( "Multiplying and dividing by 6 we get a more popular way of expressing the solutions, which can be further simplified
\n" ); document.write( " $\"X=%286%2B-+sqrt%2896%29%29%2F6=%286%2B-+4sqrt%286%29%29%2F6=%283%2B-+2sqrt%286%29%29%2F3\"$
\n" ); document.write( "The x-intercepts are the points with the above values for x and Y=0. \n" ); document.write( "

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