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Question 1209271: Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 5x^2 + 17x + 20.
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! **1. Combine Like Terms**
* y = -2x² + 8x - 15 - 5x² + 17x + 20
* y = -7x² + 25x + 5
**2. Find the Vertex**
* **Vertex Formula:** For a parabola in the form y = ax² + bx + c, the vertex is given by:
* x-coordinate of the vertex: x = -b / 2a
* **In this case:**
* a = -7
* b = 25
* x = -25 / (2 * -7) = 25/14
* **Find the y-coordinate of the vertex:**
* Substitute the x-coordinate of the vertex back into the equation:
* y = -7(25/14)² + 25(25/14) + 5
* y = -7(625/196) + 625/14 + 5
* y = -225/28 + 625/14 + 5
* y = 225/7 + 5
* y = 265/7
**Therefore, the vertex of the graph is (25/14, 265/7).**
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