Linear, Quadratic and Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically expressed in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax² + bx + c can be found using the formula x = -b/(2a). Substitute this x-value back into the function to find the y-coordinate.

Front

What does it mean for a graph to open up or down?

Back

A quadratic graph opens up if the coefficient of x² (a) is positive and opens down if a is negative.

Front

What is the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found at the vertex of the parabola, which is the highest point when the graph opens down.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of y when x = 0.

Front

How can you determine if a function is linear, quadratic, or exponential?

Back

Examine the equation: if it is of the form y = mx + b, it is linear; if it is y = ax² + bx + c, it is quadratic; if it is y = ab^x, it is exponential.

Front

What is the formula for the height of a projectile?

Back

The height h of a projectile can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

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

Back

Linear functions graph to straight lines and have a constant rate of change, while quadratic functions graph to parabolas and have a variable rate of change.