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МатематикаВопрос:
Which graph corresponds to the equation y = x² + 7x + 14?
Ответ:
Match the equation to its graph:
Quick Explanation: To match the equation y = x² + 7x + 14 to its graph, we need to analyze the properties of the parabola, such as its vertex and direction of opening. Since the coefficient of x² is positive (1), the parabola opens upwards. We can find the x-coordinate of the vertex using the formula x = -b/(2a).
Step-by-step solution:
- Analyze the equation: The given equation is y = x² + 7x + 14. Here, a = 1, b = 7, and c = 14.
- Determine the direction of opening: Since 'a' (the coefficient of x²) is positive (a = 1), the parabola opens upwards. This eliminates graph 'B' which opens downwards.
- Calculate the x-coordinate of the vertex: Using the formula x = -b/(2a), we get x = -7 / (2 * 1) = -7/2 = -3.5.
- Calculate the y-coordinate of the vertex: Substitute x = -3.5 into the equation: y = (-3.5)² + 7*(-3.5) + 14 = 12.25 - 24.5 + 14 = 1.75. So, the vertex is at (-3.5, 1.75).
- Compare with the graphs: Graph 'A' shows a parabola opening upwards with its vertex approximately at (-3.5, 1.75). Graph 'Б' opens upwards but its vertex appears to be at (3.5, 1.75) or similar positive x-value. Graph 'B' opens downwards.
Answer: Graph A corresponds to the equation y = x² + 7x + 14.
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