Write linear quadratic and exponential functions

Learning Objectives Identify a function as linear, quadratic, or exponential by analyzing the pattern in a table of values. Write a linear function in the form y = mx + b given a table of values or two points. Write an exponential function in the form y = a(b)^x given a table of values. Write a quadratic function in the form y = ax^2 + bx + c given a table of values. Determine the key parameters (slope, y-intercept, common difference, common ratio, initial value) from a given data set. Model a real-world scenario by writing the appropriate linear, quadratic, or exponential function. Ever notice how a simple savings account grows steadily, but a viral video's views explode overnight? 📈💥 That's the power of different mathematical functions at work! In this tutoria...

TermDefinitionExample Linear FunctionA function that has a constant rate of change. In a table with evenly spaced x-values, the 'first differences' (the difference between consecutive y-values) are constant.y = 2x + 5. For every 1-unit increase in x, y increases by a constant value of 2. Quadratic FunctionA function that creates a U-shaped curve (a parabola). In a table, the 'second differences' (the differences between the first differences) are constant.y = x^2 + 2x + 1. The rate of change is not constant, but the rate of the rate of change is. Exponential FunctionA function where for each unit increase in x, the y-value is multiplied by a constant factor, called the common ratio.y = 3(2)^x. For every 1-unit increase in x, the y-value doubles. First DifferencesThe va...

Linear Function: Slope-Intercept Form y = mx + b Used for linear functions. 'm' is the slope, which is the same as the constant first difference. 'b' is the y-intercept, which is the value of y when x = 0. Exponential Function: Standard Form y = a(b)^x Used for exponential functions. 'a' is the initial value, which is the value of y when x = 0. 'b' is the common ratio. Quadratic Function: Standard Form y = ax^2 + bx + c Used for quadratic functions. 'c' is the y-intercept (y when x=0). The value of 'a' is half of the constant second difference (a = second difference / 2). The value of 'b' can be found by substituting a known point into the equation.