Modeling Quadratic Functions: Graphs and Equations

The video tutorial explains how to model quadratic functions by drawing graphs and writing equations. It begins with a comparison of linear and quadratic functions, emphasizing the use of slope-intercept form for linear functions. The concept of squaring numbers is introduced, leading to the explanation of quadratic patterns. The tutorial demonstrates how to graph quadratic functions and highlights their differences from linear functions, such as their curved shape and symmetry. Finally, it provides a problem-solving example using quadratic equations and graphing techniques.

What is the primary difference between a linear function and a quadratic function?

• A linear function is represented by a curve, while a quadratic function is a straight line.

• A linear function grows by equal differences over equal intervals, while a quadratic function does not.

• A quadratic function is always decreasing, while a linear function is always increasing.

• A quadratic function is represented by a horizontal line, while a linear function is a vertical line.

What is the shape of the graph of a quadratic function like y = X^2?

• A straight line

• A circle

• A parabola

• A hyperbola

Which of the following is a characteristic of the graph of y = X^2?

• It is asymmetrical over the Y axis.

• It is symmetrical over the Y axis.

• It decreases more quickly than a line.

• It goes below the X axis.

What is the equation of the quadratic function that shifts the graph of y = X^2 down by 2 units?

• y = X^2 + 2

• y = X^2 - 2

• y = X^2 * 2

• y = X^2 / 2

How do you graph a quadratic function like y = X^2 - 2?

• Plot the points and connect them with a straight line.

• Plot the points and connect them with a dotted line.

• Plot the points and connect them with a smooth curve.

• Plot the points and connect them with a zigzag line.