1. Warm-up

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 When and at what height does the flare and the rocket meet?

3. 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 Can the gull catch the crab before it hits the water? Justify your answer.

4. Homework Answers

5. Homework Answer $1

6. Solving Nonlinear Systems Lines and Circles

7. 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.
Examples
no solution 1 solution 2 solutions

8. Find the points of intersection
x2 + y2 = & y = x + 1
We will use….. Substitution.
Now plug these values into the
Equation to get y!!
(-3,-2) and (2,3) are the points
where the two graphs intersect.
Check it on your calculator!

9. Solve by substitution:

10. Let’s see how we are doing...

11. The sum of two numbers is 24
The sum of two numbers is 24. The sum of the squares of the two numbers is What is the product of the two numbers?

12. A circular pond is modeled by the equation x2+y2=225
A circular pond is modeled by the equation x2+y2=225. A bridge over the pond is modeled by a segment of the equation x-7y=-75. What are the coordinates of the points where the bridge meets the edge of the pond?