Linear, Exponential, Quadratic: Which is it?

What is a quadratic function?

• A polynomial function of degree 1

• A polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where 'a', 'b', and 'c' are constants and 'a' is not zero.

• A linear function represented by a straight line

• A function that has a constant value for all inputs

What does the graph of a linear function look like?

• The graph of a linear function is a straight line that can slope upwards or downwards.

• The graph of a linear function is a curved line that represents a quadratic equation.

• The graph of a linear function is a series of points scattered randomly on a plane.

• The graph of a linear function is a zigzag line that alternates direction.

What is a real-world example of a quadratic function?

• The trajectory of a projectile, such as a ball thrown into the air, which follows a parabolic path.

• The speed of a car moving in a straight line at constant velocity.

• The growth of a population in a linear fashion over time.

• The relationship between the distance traveled and time taken for a train moving at a constant speed.

What is the y-intercept in a linear function?

• The point where the graph crosses the x-axis.

• The point where the graph crosses the y-axis, represented by the value of 'b' in the equation f(x) = mx + b.

• The slope of the line in the equation f(x) = mx + b.

• The value of 'm' in the equation f(x) = mx + b.

What is exponential decay?

• A decrease in a quantity at a rate proportional to its current value, typically modeled by the function f(x) = a * e^(-bx) where 'a' and 'b' are constants.

• An increase in a quantity at a rate proportional to its current value, typically modeled by the function f(x) = a * e^(bx) where 'a' and 'b' are constants.

• A constant decrease in a quantity over time, represented by a linear function.

• A random fluctuation in a quantity that does not follow a predictable pattern.

What is the difference between linear and quadratic functions?

• Linear functions have a constant rate of change and produce straight-line graphs, while quadratic functions have a variable rate of change and produce parabolic graphs.

• Linear functions can produce parabolic graphs, while quadratic functions always produce straight-line graphs.

• Linear functions have a variable rate of change, while quadratic functions have a constant rate of change.

• Linear functions are always increasing, while quadratic functions can be increasing or decreasing.

What is the significance of the vertex in a quadratic function?

• It represents the x-intercepts of the function.

• It is the point where the graph changes direction.

• The vertex is the highest or lowest point on the graph, representing the maximum or minimum value of the function.

• It indicates the slope of the function.

What is the general form of an exponential growth equation?

• y = a * b^x, where 'a' is the initial value and 'b' is the growth factor.

• y = a + b * x, where 'a' is the initial value and 'b' is the slope.

• y = a - b^x, where 'a' is the initial value and 'b' is the decay factor.

• y = a / b^x, where 'a' is the initial value and 'b' is the growth factor.

What is a linear function?

• A polynomial function of degree 1, represented by the equation f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

• A function that graphs to a parabola and has a degree of 2.

• A function that has a constant rate of change and is represented by a quadratic equation.

• A function that can be represented by a piecewise equation with multiple segments.

How can you identify a quadratic function from its equation?

• A quadratic function has a constant term only.

• A quadratic function can be identified by the presence of the x^2 term in its equation, indicating that the highest degree of x is 2.

• A quadratic function has a degree of 1.

• A quadratic function can be identified by the presence of the x term only.