document.write( "Question 184808This question is from textbook Algebra and Trigonometry Structure and Method book 2
\n" ); document.write( ": I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!\r
\n" ); document.write( "\n" ); document.write( "Find all intercepts of the parabola y-2=-1/2(x-4)^2 \n" ); document.write( "

Algebra.Com's Answer #138760 by jojo14344(1513) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Given: $\"y-2=-1%2F2%28x-4%29%5E2\"$ ---> $\"y-2=%28-1%2F2%29%28x%5E2-8x%2B16%29\"$ , distribute $\"-1%2F2\"$ and transfer $\"-2\"$ to the right.
\n" ); document.write( " $\"y=%28-1%2F2%29x%5E2-%28-8%2F2%29x%2B%28-16%2F2%29%2B2=%28-1%2F2%29x%5E2%2B4x-8%2B2\"$
\n" ); document.write( " $\"y=%28-1%2F2%29x%5E2%2B4x-6\"$ , EQN 1
\n" ); document.write( "First, we'll find the vertex thru Vertex form: $\"y=a%28x-h%29%5E2%2Bk%5E2\"$
\n" ); document.write( "where $\"system%28h=x%2Ck=y%29\"$ of the vertex
\n" ); document.write( "we complete the square:
\n" ); document.write( "Divide the whole eqn by $\"-1%2F2\"$ :
\n" ); document.write( " $\"y%2F%28-1%2F2%29=%28%28-1%2F2%29x%5E2%2B4x-6%29%2F%28-1%2F2%29\"$ --->
\n" ); document.write( " $\"-2y=x%5E2-8x%2B12\"$
\n" ); document.write( " $\"-2y=%28x%5E2-8x%2Bhighlight%2816%29%29%2B12-highlight%2816%29\"$
\n" ); document.write( " $\"-2y=%28x-4%29%5E2-4\"$
\n" ); document.write( " $\"cross%28-2%29y%2Fcross%28-2%29=%28%28x-4%29%5E2-4%29%2F-2\"$
\n" ); document.write( " $\"y=%28-1%2F2%29%28x-4%29%5E2-%284%2F-2%29\"$
\n" ); document.write( " $\"y=%28-1%2F2%29%28x-4%29%5E2%2B2\"$
\n" ); document.write( "You see, $\"highlight%28h=x=4%29\"$ & $\"highlight%28k=y=2%29\"$ --->VERTEX (4,2)
\n" ); document.write( "Next:
\n" ); document.write( "Let $\"Fx=0\"$ , as per EQN 1
\n" ); document.write( " $\"y=%28-1%2F2%29%280%29%5E2%2B4%280%29-6\"$
\n" ); document.write( " $\"highlight%28y=-6%29\"$ , Y Intercept
\n" ); document.write( "Next:
\n" ); document.write( "For the X Intercepts, we solve the Eqn1:
\n" ); document.write( "by QUADRATIC, where $\"system%28a=-1%2F2%2Cb=4%2Cc=-6%29\"$
\n" ); document.write( "Solving for he discriminant: $\"b%5E2-4ac=4%5E2-4%28-1%2F2%29%28-6%29=16-12=4\"$
\n" ); document.write( "Therefore,
\n" ); document.write( " $\"x=%28-4%2B-sqrt%284%29%29%2F%282%2A-1%2F2%29=%28-4%2B-2%29%2F-1\"$
\n" ); document.write( " $\"x=%28-4%2B2%29%2F-1=-2%2F-1=highlight%282%29\"$
\n" ); document.write( "Also, $\"x=%28-4-2%29%2F-1=-6%2F-1=highlight%286%29\"$
\n" ); document.write( "Then we see the graph, plotting all intercepts:
\n" ); document.write( "
\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo \n" ); document.write( "

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