answer:
The equation Y = -50(x-14)^2 + 800 represents a quadratic function in vertex form.
Let's analyze the equation step by step:
1. The vertex form of a quadratic function is Y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
2. Comparing the given equation to the vertex form, we can determine the following information:
- The vertex of the parabola is located at the point (14, 800).
- The coefficient "a" determines the shape and direction of the parabola.
3. In this case, the coefficient "a" is -50, which means the parabola opens downward since it is negative.
4. The vertex (h, k) is (14, 800), which represents the highest point of the parabola.
Therefore, based on the equation Y = -50(x-14)^2 + 800, we can conclude that the parabola opens downward and its highest point (vertex) is located at (14, 800).
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To solve the equation Y = -50(x-14)^2 + 800 for y, we need to isolate y on one side of the equation.
Here are the steps to solve for y:
1. Start with the given equation: Y = -50(x-14)^2 + 800
2. Replace Y with y to match the variable we want to solve for: y = -50(x-14)^2 + 800
3. Apply the order of operations, performing the operations inside the parentheses first: y = -50(x^2 - 28x + 196) + 800
4. Distribute -50 to the terms inside the parentheses: y = -50x^2 + 1400x - 9800 + 800
5. Simplify the equation: y = -50x^2 + 1400x - 9000
Now, the equation is in the form y = -50x^2 + 1400x - 9000. This equation represents a quadratic function.
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