Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like '≥', '≤', '>', or '<'. In this case, the inequality -x² + 4x + 1 ≥ 0 indicates that we are looking for values of x that make the quadratic expression non-negative. Understanding how to manipulate and solve inequalities is crucial for finding the solution set.
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Quadratic Functions
A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax² + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'. In this problem, the quadratic -x² + 4x + 1 will be analyzed to determine where it is greater than or equal to zero.
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Solving Quadratic Equations Using The Quadratic Formula
Interval Notation
Interval notation is a mathematical notation used to represent a range of values on the number line. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, the interval [a, b) includes 'a' but not 'b'. Writing the solution set of the inequality in interval notation is essential for clearly communicating the range of x values that satisfy the inequality.
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