Question 71·Medium·Nonlinear Equations in One Variable; Systems in Two Variables
A system of equations consists of a line and a parabola. The graphs of the two equations are shown in the -plane.
The solutions to the system are the points where the graphs intersect. Which choice is the distance between the two solutions?
For system-of-equations graph questions, first identify what the solution represents (here, the intersection points). Read those coordinates carefully from the grid, then apply the needed algebraic tool—in this case, the distance formula using the changes in and between the two solutions.
Hints
Identify the solutions
The solutions to the system are where the two graphs cross each other. Find both intersection points.
Write down the coordinates
Read the - and -coordinates of each intersection point from the grid.
Distance between two points
Once you have the two points and , use .
Desmos Guide
Enter the intersection points
In Desmos, define the points you read from the graph:
A=(-1,0)
B=(2,3)
Calculate the distance
In a new line, type:
d=sqrt((x(B)-x(A))^2+(y(B)-y(A))^2)
Then simplify the value of (it will appear as an exact expression).
Step-by-step Explanation
Read the solutions from the graph
From the graph, the line and the parabola intersect at the points and .
Use the distance formula
Use the distance formula between and :
Compute the distance
So the distance between the two solutions is .