Consider the quadratic function [tex]$f(x)=-2 x^2+5 x-4$[/tex].
The leading coefficient of the function is $\square$
Answer (1)
Identify the quadratic function: f ( x ) = − 2 x 2 + 5 x − 4 .
Recognize the leading coefficient as the coefficient of the x 2 term.
The leading coefficient is − 2 .
Explanation
Identifying the Leading Coefficient We are given the quadratic function f ( x ) = − 2 x 2 + 5 x − 4 . The leading coefficient of a quadratic function in the form a x 2 + b x + c is the coefficient of the x 2 term, which is a . In this case, a = − 2 .
Final Answer Therefore, the leading coefficient of the given quadratic function is − 2 .
Examples
Understanding the leading coefficient helps in predicting the parabola's direction (upward or downward) and its stretch. For example, in physics, the height of a projectile over time can be modeled by a quadratic function. The leading coefficient would indicate whether gravity is acting to pull the object down (negative coefficient) or if some force is pushing it upwards (positive coefficient, though not physically realistic in this scenario). Knowing the leading coefficient helps in analyzing the trajectory and making predictions about the projectile's motion.
