document.write( "Question 887945: A parabola has intercepts of x = -2, x = 3, and y = -4.\r
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\n" ); document.write( "\n" ); document.write( "f. Graph the parabola. Label axis, vertex, and intercepts.
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Algebra.Com's Answer #536982 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
A parabola has intercepts of x = -2, x = 3, and y = -4.
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document.write( "Therefore it passes through the points (-2,0), (3,0), and (0,-4).\r\n" );
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document.write( "We plot those and sketch the graph approximately going through those\r\n" );
document.write( "three points\r\n" );
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\n" ); document.write( "a. Write the intercept form of the parabola.
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document.write( "x=-2 becomes x+2=0 and x=3 becomes x-3=0\r\n" );
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document.write( "The intercept form is \r\n" );
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document.write( "y = a(x+2)(x-3)\r\n" );
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document.write( "because when you set that = 0 you get the x-intercepts x=-2 and x=3\r\n" );
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\n" ); document.write( "b. State the direction of the parabola. Explain.
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document.write( "Looking at the graph above we can see that it can only open upward.           \r\n" );
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\n" ); document.write( "c. Write in ax2 + bx + c form.
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document.write( "We take the intercept form and substitute the y-intercept (0,-4)\r\n" );
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document.write( " y = a(x+2)(x-3)\r\n" );
document.write( "-4 = a(0+2)(0-3)\r\n" );
document.write( "-4 = a(2)(-3)\r\n" );
document.write( "-4 = -6a\r\n" );
document.write( "\"%28-4%29%2F%28-6%29\" = a\r\n" );
document.write( "\"2%2F3\" = a\r\n" );
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document.write( "[Note: We could have answered b above without looking at\r\n" );
document.write( "the graph because if a is positive the graph opens\r\n" );
document.write( "upward and if negative it opens downward]\r\n" );
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document.write( "Substitute for a:\r\n" );
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document.write( " y = \"2%2F3\"\"%28x%2B2%29%28x-3%29\"\r\n" );
document.write( " y = \"2%2F3\"\"%28x%5E2-x-6%29\"\r\n" );
document.write( " y = \"expr%282%2F3%29x%5E2-expr%282%2F3%29x-4\"\r\n" );
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\n" ); document.write( "e. What is the vertex?
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document.write( "We use the vertex formula:\r\n" );
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document.write( "The vertex is the point with x-coordinate \"-b%2F%282a%29\" = \r\n" );
document.write( "\"-%28-2%2F3%29%2F%282%282%2F3%29%29\"\"%22%22=%22%22\"\"%282%2F3%29%2F%284%2F3%29\"\"%22%22=%22%22\"\"%282%2F3%29%2A%283%2F4%29\"\"%22%22=%22%22\"\"1%2F2\"\r\n" );
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document.write( "The y-coordinate of the vertex is found by substituting \"x=1%2F2\" into the\r\n" );
document.write( "original equation:\r\n" );
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document.write( " y = \"expr%282%2F3%29x%5E2-expr%282%2F3%29x-4\"\r\n" );
document.write( " y = \"%282%2F3%29%281%2F2%29%5E2-%282%2F3%29%281%2F2%29-4\"\r\n" );
document.write( " y = \"%282%2F3%29%281%2F4%29-%281%2F3%29-4\"\r\n" );
document.write( " y = \"1%2F6-1%2F3-4\"\r\n" );
document.write( " y = \"1%2F6-2%2F6-24%2F6\"\r\n" );
document.write( " y = \"-25%2F6\"\r\n" );
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document.write( "So the vertex is \"%28matrix%281%2C3%2C1%2F2%2C%22%2C%22%2C-25%2F6%29%29\", which is the\r\n" );
document.write( "red point at the bottom of the graph below.\r\n" );
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\n" ); document.write( "d. What is the axis of symmetry?
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document.write( "The axis of symmetry is the vertical line whose equation is x=h, \r\n" );
document.write( "where h is the x-coordinate of the vertex. In this case it is \"x=1%2F2\".\r\n" );
document.write( "It is the vertical line passing through the vertex.\r\n" );
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document.write( "Axis of symmetry \"x=1%2F2\", the green vertical line below:\r\n" );
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document.write( "Edwin
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