A formula for approximating the stopping distance, d, in...

A formula for approximating the stopping distance, $d$, in feet, for a specific car on dry pavement is $d=\frac{1}{10} x^{2}$, where $x$ is the speed of the car, in miles per hour, before the brakes are applied. If the car's stopping distance was 90 feet, what was the car's speed before the brakes were applied?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Quadratic Functions

A quadratic function is a second-degree polynomial that involves a variable raised to the power of two. Such functions commonly arise in modeling scenarios where the relationship between two quantities is non-linear, such as when one quantity is proportional to the square of another. Understanding the structure of quadratic functions is crucial for identifying how changes in one variable affect another in various practical contexts.

Algebraic Manipulation

Algebraic manipulation refers to the process of rearranging and simplifying equations to isolate the desired variable. This includes operations such as multiplying, dividing, adding, subtracting, and taking roots, which are fundamental skills needed to solve equations and derive meaningful conclusions from mathematical models.

Square Root Principle

The square root principle is applied in solving equations where a variable is squared. Once an equation is simplified to the form where a squared term equals a number, taking the square root of both sides allows for finding the variable’s value. In real-world applications, it’s important to consider the context to ensure that only the physically meaningful (often positive) solution is used.

Transcript

Please give Ace some feedback