Linear and Quadratic Systems

Match the following

• where the parabola & line intersect

• If the parabola & line don't intersect at all, there are

• 2 solutions

• If the parabola & line intersect 2 times, there are

• 0 solutions

• If the parabola & line intersect 1 time, there is

• 1 solution

• Looking at a graph, the solutions to a linear-quadratic system are:

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions

• 1 solution

• 2 solutions

• 3 solutions

Answer explanation

The solutions are the coordinate points where the parabola and line intersect.

What are the solutions to the graphed system?

• (0,-2) and (-3,1)

• (-2,0) and (2,0)

• (0,-2) and (3,1)

• (2,2) and (1,0)

Answer explanation

The solutions are the coordinate points where the parabola and line intersect.

• A

• B

• C

• D

Answer explanation

The solutions are the coordinate points where the parabola and line intersect.

Graph in desmos to find the solution(s):
y = x² - 4x + 6
y = x + 2

• (3, 1) and (6, 4)
• (-1, 1) and (4, 2)
• (1, 3) and (4, 6)
• (1, 4) and (3, 6)

How many solutions does this system of equations have?

• one solution

• two solutions

• no solutions

• All of the above

How many solutions does this system of equations have?

• one solution

• two solutions

• three solutions

• no solutions

Determine the solution to the given linear-quadratic function.

• (0, 0)
• (3, 0)
• (2, -3)
• (-3, 2)

The system of a linear and a quadratic function can have the following number of solutions, EXCEPT

• No solution
• 1 solution
• 2 solutions
• more than 2 solutions

Graph on desmos to find the solutions to the system:
y = x² + 3x - 5
y = x + 3

• (-4, 2) and (-1, 5)
• (-4, -1) and (2, 5)
• (2, -1 and (-4, 5)
• (-4, 1) and (2, -1)