Transcript Warm Spring Night

Warm-up
2
2
x

y
2x substitution:
6y  26
1) Solve the systemusing
3y - 2x = 11
2) Given the inequality
and the graph, shade
appropriately.
y + 2x = 9
y £ x 2 + 4x + 8
Application Problem
The amount of money that a freshman class fundraiser can raise
can be modeled by the inequality y≤-2x2 + 16x – 24, where x
represents the number of days into the sale and y represents the
amount of money raised in hundreds.
a) Graph
b) What is the max?
What does it represent?
c) When will they start
to raise money
d) How many days should
the fundraiser last?
e) On which days will the sale make more than $400?
Solving
Nonlinear Systems
If the graphs of a system of equations are a conic section and
a straight line, the system will have zero, one, or two
solutions.
no solution
1 solution
2 solutions
• We’ve already studied
techniques for solving systems of
linear equations.
• You will use these same
techniques to solve quadratic
systems.
• These techniques are ???
• Substitution, Elimination, Graphing
Find the points of intersection
• y = x2 +2x+4 & y = 6x + 1
• We will use….. Substitution.
Now plug these values into the
Equation to get y!!
(3,19) and (1,7) are the points
where the two graphs intersect.
Check it on your calculator!
Solve by substitution or Elimination:
x2 - y = 5
y + 10x = 30
-3x + y = -7
y=x2 + 7x + 100
You Try!
y = 5x - 20
2
y=x - 10x + 25
y = -x - 7
y = x - 4x - 5
2
x + 2y = 4
y = x - 6x + 8
2
A rocket is launched from the ground and
follows a parabolic path represented by the
equation y = -x2 + 10x. At the same time, a
flare is launched from a height of 10 feet and
follows a straight path represented by the
equation y = -x + 10. When and at what
height does the flare and the rocket meet?
A pelican flying in the air over water drops a
crab from a height of 30 feet. The distance
the crab is from the water as if falls can be
represented by the function h(t) = -16t2 + 30,
where t is time, in seconds. To catch the crab
as it falls, a gull flies along a path represented
by the function g(t) = -8t + 15. Can the gull
catch the crab before it hits the water? Justify
your answer.
Calling All Superheroes
This will be your first project.
It will be due September 17th at the beginning of
class.
It will involve not only math but writing and some
creativity.
Do NOT wait until 16th to try to start and finish this
assignment. It will be a quiz grade that will not be
replaced by a test.