Algebra 2 Quadratic Modeling and Motion

Questions and Answers

What is the projectile motion equation?

H(t)=16t^2 + vt + h

What does the variable V represent in the context of projectile motion?

Initial velocity

What does the variable H represent in the context of projectile motion?

Initial height (feet)

What changes in the projectile motion equation when using meters?

-4.9t^2 Signup and view all the answers

What is the calculator menu option for quadratic modeling?

Menu 3 2 Signup and view all the answers

What is the calculator menu option for factoring?

Menu 3 3 3 Signup and view all the answers

How do you find a quadratic modeling equation?

Use ax^2 + bx + c, plug in the x, plug equations into calc and replace a, b, c with x, y, z Signup and view all the answers

What is the height of the arch in a quadratic equation?

Vertex (use calc) Signup and view all the answers

What is the formula for the discriminant?

b^2-4ac Signup and view all the answers

What is a linear function?

A function whose graph is a straight line. Signup and view all the answers

What is a quadratic function?

y=x^2 Signup and view all the answers

Study Notes

Projectile Motion and Quadratics

The projectile motion equation is represented as H(t) = 16t² + vt + h, where H is height at time t.
The term 'v' denotes initial velocity, specifying how fast the object moves at the start.
The initial height, represented by 'h', indicates the starting position from which the object is launched, measured in feet.

Units and Calculator Functions

When converting the projectile motion equation for meters, the equation changes to H(t) = -4.9t² + vt + h.
To access quadratic modeling capabilities on a calculator, navigate to Menu 3, then select option 2.
For factoring quadratic expressions, the appropriate calculator function is found under Menu 3, then proceed to 3, and finally select 3 again.

Finding Quadratic Modeling Equations

The general form to find a quadratic modeling equation is ax² + bx + c; inputting values allows for calculation of coordinates.
After finding a, b, and c, substitute x, y, and z in the equations to analyze and graph the function.

Key Concepts in Quadratic Functions

The vertex of a parabola, which represents the maximum or minimum height, can be found using the calculator.
The discriminant, calculated as b² - 4ac, helps determine the nature of the roots of the quadratic equation.
A linear function graphs as a straight line, while a quadratic function is defined by the equation y = x², creating a parabolic shape.

Description

Explore the key concepts of projectile motion and quadratic modeling in Algebra 2. This quiz covers essential equations, such as the projectile motion equation, and introduces important variables like initial velocity and height. Perfect for reinforcing your understanding of these topics.