document.write( "Question 1209271: Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 5x^2 + 17x + 20. \n" ); document.write( "
Algebra.Com's Answer #848036 by asinus(45)\"\" \"About 
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**1. Combine Like Terms**\r
\n" ); document.write( "\n" ); document.write( "* y = -2x² + 8x - 15 - 5x² + 17x + 20
\n" ); document.write( "* y = -7x² + 25x + 5\r
\n" ); document.write( "\n" ); document.write( "**2. Find the Vertex**\r
\n" ); document.write( "\n" ); document.write( "* **Vertex Formula:** For a parabola in the form y = ax² + bx + c, the vertex is given by:
\n" ); document.write( " * x-coordinate of the vertex: x = -b / 2a\r
\n" ); document.write( "\n" ); document.write( "* **In this case:**
\n" ); document.write( " * a = -7
\n" ); document.write( " * b = 25
\n" ); document.write( " * x = -25 / (2 * -7) = 25/14\r
\n" ); document.write( "\n" ); document.write( "* **Find the y-coordinate of the vertex:**
\n" ); document.write( " * Substitute the x-coordinate of the vertex back into the equation:
\n" ); document.write( " * y = -7(25/14)² + 25(25/14) + 5
\n" ); document.write( " * y = -7(625/196) + 625/14 + 5
\n" ); document.write( " * y = -225/28 + 625/14 + 5
\n" ); document.write( " * y = 225/7 + 5
\n" ); document.write( " * y = 265/7\r
\n" ); document.write( "\n" ); document.write( "**Therefore, the vertex of the graph is (25/14, 265/7).**
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