A ball is thrown upward with an initial velocity such that its height in meters after seconds is given by the equation . To find the time at which the ball reaches its maximum height, you need to complete the square. t = _____.
Answer & Analysis
Analysis
Question Analysis
This problem tests the application of completing the square to a real-world scenario involving a quadratic function.
Key Concept Explanation
Completing the square can be used to find the vertex of a parabola, which in this context gives the time at which the ball reaches its maximum height.
Step-by-step Solution
Factor out the coefficient of from the first two terms:
Complete the square inside the parentheses by adding and subtracting :
Simplify the expression:
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