Math Problem Statement
Use the same scales and axes to draw the graphs of the two functions f(x) = 2 + 2x + x^2 and g(x) = 5 - 2x - x^2 in the domain -3 ≤ x ≤ 2, x ∈ R. (a) Use your graphs to estimate the values of x for which f(x) = g(x). (b) Use your graphs to estimate the values of x for which f(x) ≥ g(x).
Solution
The intersection points, where , are approximately:
Answers for each part:
- (a) The values of for which are approximately and .
- (b) For , the intervals can be estimated from the graph. It appears that when .
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Math Problem Analysis
Mathematical Concepts
Algebra
Graphing Functions
Quadratic Equations
Formulas
Quadratic functions f(x) = ax^2 + bx + c
Theorems
Intersection of functions
Suitable Grade Level
Grades 9-12
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