A quadratic function has the form . If the function passes through the points (1, 6), (2, 11), and (3, 18), find the value of b.
Answer & Analysis
Analysis
Question Analysis
This question requires students to use the given points to set up a system of equations and solve for the coefficients of the quadratic function.
Key Concept Explanation
A quadratic function in the form can be determined by substituting the given points into the equation and solving the resulting system of equations.
Step-by-step Solution
1. Substitute the points (1, 6), (2, 11), and (3, 18) into the equation .
2. Set up the system of equations:
For (1, 6):
For (2, 11):
For (3, 18):
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