Linear and Parabolic Systems

What is the solution to the system of equations show:

How many solutions does this system of equations have?

Solve the system above.

• (1,5)

• (5,-2)

• (-2,5)

• (5,1)

Lava coming from the eruption of a volcano follows a parabolic path.  The height h in feet of a piece of lava t seconds after it is ejected from the volcano is given by h(t) = -t² + 16t + 936.  After about how many seconds does the lava reach its maximum height?

• 12

• 20

• 8

• 5

If a nonlinear system contains a linear function that never touches the quadratic function, that system has...

• 2 solutions

• 1 solution

• No solutions

• Infinite solutions

When solving a system algebraically, which expression indicates there is 1 solution?

• 2=2

• -2=6

• x=7

• 0=0

Compare ƒ(x) = -2x² - 8x + 20 to the graph of g(x) shown.  What can you conclude about the two functions?

•  ƒ(x) has a greater maximum than g(x).

• g(x) has a greater maximum than ƒ(x).

• ƒ(x) has a minimum, while g(x) has a maximum.

• g(x) and ƒ(x) have the same maximum.

Which scenario could be modeled by a linear function?

• the population of a city that is growing by 3% each year

• the amount of carbon in a sample that is decaying by half every 6 hours

• the number of calories burned when running at a constant speed

• the height of a rocket 6 hours after takeoff

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)