Standard #: MAFS.912.A-REI.4.11 (Archived Standard)

Students are asked to use technology (e.g., spreadsheet, graphing calculator, or dynamic geometry software) to estimate the solutions of the equation f(x) = g(x) for given functions f and g.

Students are asked to find the solution(s) of the equation f(x) = g(x) given the graphs of f and g and explain their reasoning.

Students are asked to find solutions of the equation f(x) = g(x) for two given functions, f and g, by constructing a table of values.

Students are asked to explain why the x-coordinate of the intersection of two functions, f and g, is a solution of the equation f(x) = g(x).

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a coaster's height and speed. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation. This lesson also uses prior knowledge and has students solve systems of equations graphically to determine which type of coaster is faster.

Follow as we learn why the x-coordinate of the point of intersection of two functions is the solution of the equation f(x) = g(x) in this interactive tutorial.

In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11).

This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers.

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

Follow as we learn why the x-coordinate of the point of intersection of two functions is the solution of the equation f(x) = g(x) in this interactive tutorial.

In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11).

This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers.

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11).

This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers.