document.write( "Question 184808This question is from textbook Algebra and Trigonometry Structure and Method book 2
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Algebra.Com's Answer #852480 by MathTherapy(10560)\"\" \"About 
You can put this solution on YOUR website!
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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? \r\n" );
document.write( "Please and Thank You!! I would deeply appreciate it!!\r\n" );
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document.write( "Find all intercepts of the parabola y-2=-1/2(x-4)^2\r\n" );
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document.write( "TOTALLY, TOTALLY UNNECESSARY steps by the person who responded.\r\n" );
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document.write( "\"y+-+2+=+%28-+1%2F2%29%28x+-+4%29%5E2\"\r\n" );
document.write( "\"y+=+%28-+1%2F2%29%28x+%2B+highlight%28-+4%29%29%5E2+%2B+highlight_green%282%29\" ----- Adding 2 to both sides\r\n" );
document.write( "\"y+=+a%28x+%2B+highlight%28-+h%29%29%5E2+%2B+highlight_green%28+k%29\" ----- Vertex form of a parabola, where the VERTEX, (h, k) = (4, 2)\r\n" );
document.write( "\"h\" is the x-coordinate of the vertex of the parabola, is also the paeabola's Axis of Symmetry, as well as the MIDWAY point\r\n" );
document.write( "between the x-intercepts.\r\n" );
document.write( "If MiDWAY between 2 points of a HORIZONTAL line is 4, then LEFT and RIGHT endpoints are: \"4+-+4%2F2+=+4+-+2+=+2\", and \"4+%2B+4%2F2+=+4+%2B+2+=+6\".\r\n" );
document.write( "Therefore, x-intercepts are 2 and 6, or at the coordinate points: (2, 0) and (6, 0).\r\n" );
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document.write( "Although more time-consuming, we can also do the following:\r\n" );
document.write( "\"y+-+2+=+%28-+1%2F2%29%28x+-+4%29%5E2\"\r\n" );
document.write( "\"y+=+%28-+1%2F2%29%28x+-+4%29%5E2+%2B+2\" ---- Adding 2 to both sides\r\n" );
document.write( "\"y+=+%28-+1%2F2%29%28x%5E2+-+8x+%2B+16%29+%2B+2\"\r\n" );
document.write( "\"0+=+%28-+1%2F2%29%28x%5E2+-+8x+%2B+16%29+%2B+2\" ---- Substituting 0 for y, since y-values on x-axis are 0\r\n" );
document.write( "- 2(0) = \"-+2%28%28-+1%2F2%29%28x%5E2+-+8x+%2B+16%29+%2B+2%29%29\" ---- Multiplying each side by - 2\r\n" );
document.write( "\"matrix%281%2C3%2C+0+=+x%5E2+-+8x+%2B+16+-+4%2C+or%2C+x%5E2+-+8x+%2B+12+=+0%29\"\r\n" );
document.write( "(x - 2)(x - 6) = 0 ---- Factorizing the trinomial\r\n" );
document.write( "x - 2 = 0       OR      x - 6 = 0\r\n" );
document.write( "x = 2           OR      x = 6\r\n" );
document.write( "x-INTERCEPTS: (2, 0) (6, 0)
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