4.9 Systems of Quadratic Equations

What are 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)

Find the solution:
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)

Amy throws a quarter from the top of a building at the same time that a balloon is released from the ground. The equation describing the height y above ground of the quarter in feet is y = 64 - 2x² , where x is the time in seconds. The equation describing the elevation of the balloon in feet is y = 6x + 8, where x is the time in seconds. After how many seconds will the balloon and quarter pass each other?Check your solution for reasonableness.

• x=-7 and x=4
• 7 seconds
• 4 seconds
• 4 and 7 seconds

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

• 0 solutions
• 1 solution
• 2 solutions
• 3 solutions

Determine the solution to the given linear-quadratic function.

• (3, -1)
• (-3, 0)
• (2, -3)
• (-3, 2)

How many solutions can a line and a parabola have?

• No solutions, 1 solution
• No solutions, 1 solution, 2 solutions
• 1 solution
• No solutions, 1 solution, 2 solutions, infinite solutions

Robert threw a rock off a bridge into the river.  The distance from the rock to the river is modeled by the equation y=-16x²-16x+60, where h is the height in feet and t is time in seconds.  There is a bird flying on a path given by the equation y=5x+10.  Does the rock hit the bird?  If so, at what time and height?

• It doesn't hit the bird
• Yes, 1.23 seconds, 16.15 feet
• Yes, 16.15 seconds, 1.23 feet

Find the solution.

• (0,7) and (0,-3)
• (2,6) and (7,4)
• (3,0) and (7,4)
• (-1,5) and (-3,9)

Two equations were graphed on the set of axes below.  Which point is a solution to the system of equations ?

• (0,3)
• (5,0)
• (2,-3)
• (8,9)

How many solutions does this system of equations have?

• one solution

• two solutions

• no solutions

• All of the above