Warm-up Unit 3 Day 4 How do you graph a line? Simplify: 2𝑚+1 3 𝑔 2 −𝑚+2 3 𝑎 2 𝑏 5 𝑛 22𝑎𝑛 7 0 2𝑎𝑏 −3 2 See what you remember here… How do you graph a line? How do you graph a parabola? Solve: 2𝑥−5=3 𝑥 2 +2𝑥−8

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. Examples no solution 1 solution 2 solutions

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:

You Try!! 𝑦=5𝑥−20 𝑦= 𝑥 2 −10𝑥−20

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.