Algebra 2 Quadratic Modeling and Motion

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.