document.write( "Question 1196808: Sketch the following functions by first solving for the x intercepts using the quadratic formula. If there are no x intercepts then use the method explained in class...this makes use of the fact that raising or lowering a parabola by some amount does not change the x coordinate of the vertex. So...remove the constant from the right side, factor what's left to determine x intercepts. The average of those is the x coordinate of the vertex. Then substitute that back into the original equation to solve for the y coordinate of the vertex.
\n" ); document.write( "y = 3x^2+15x+30 AND y = -x^2+4x-8 \n" ); document.write( "

Algebra.Com's Answer #829981 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
Sketch the following functions by first solving for the x intercepts using the quadratic formula. If there are no x intercepts then use the method explained in class...this makes use of the fact that raising or lowering a parabola by some amount does not change the x coordinate of the vertex. So...remove the constant from the right side, factor what's left to determine x intercepts. The average of those is the x coordinate of the vertex. Then substitute that back into the original equation to solve for the y coordinate of the vertex.
\n" ); document.write( "y = 3x^2+15x+30 AND y = -x^2+4x-8
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First, as stated by one of the people who responded, -----------you can read the vertex and solve for the roots\"\r\n" );
document.write( "IS NOT the vertex form of the equation of: \r\n" );
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document.write( "Although prompted to use the quadratic equation formula to find the x intercepts, it's not necessary. Calculating the discriminant, , it's absolutely clear that this equation's solutions are IMAGINARY, and so, DOES NOT\r\n" );
document.write( "have any x-intercepts.\r\n" );
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document.write( "Although prompted to use the quadratic equation formula to find the x intercepts, it's not necesary. Calculating the discriminant, , it's absolutely clear that this equation's solutions are IMAGINARY, and so, DOES NOT\r\n" );
document.write( "have any x-intercepts.\r\n" );
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document.write( "I have NO IDEA what method was explained in YOUR class!!\r\n" );
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document.write( "Removing the constant, the above becomes: \r\n" );
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document.write( "                                           0 = 3x     or      0 = x + 5\r\n" );
document.write( "                                           0 = x      or    - 5 = x \r\n" );
document.write( "                               x-intercepts: 0 and - 5, or (0, 0) and (- 5, 0)\r\n" );
document.write( "x-coordinate of vertex of:  \r\n" );
document.write( "y-coordinate of vertex of: \r\n" );
document.write( "Coordinates of vertex of: 3x² + 15x + 30: (- 2.5, 11.25). \r\n" );
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document.write( "Removing the constant, the above becomes: \r\n" );
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document.write( "                                           0 = - x     or      0 = x - 4\r\n" );
document.write( "                                           0 = x       or      4 = x \r\n" );
document.write( "                               x-intercepts: 0 and 4, or (0, 0) and (4, 0)\r\n" );
document.write( "x-coordinate of vertex of:  \r\n" );
document.write( "y-coordinate of vertex of: \r\n" );
document.write( "Coordinates of vertex of: - x² + 4x - 8: (2, - 4).

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