In Exercises 69–74, solve each inequality and graph the solution set on a real number line. 2x^2 + 9x + 4 ≥ 0

Key Concepts

Inequalities

Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like ≥, ≤, >, and <. In this case, the inequality 2x^2 + 9x + 4 ≥ 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.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form ax^2 + 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 2x^2 + 9x + 4 will be analyzed to determine where it is greater than or equal to zero, which involves finding its roots and analyzing its behavior.

Graphing Solution Sets

Graphing the solution set on a real number line visually represents the values of x that satisfy the inequality. This involves marking intervals based on the roots of the quadratic and determining where the function is above or on the x-axis. Understanding how to interpret and represent solutions graphically is essential for conveying the results of the inequality effectively.