what's going on? - gilbertmath.com · linearquadratic systems 1 march 24, 2015 what's...
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LinearQuadratic Systems
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What's Going On?
Learning Goal I will be able to create quadratic functionsfrom given information.
Your Thoughts...
Think Pair Share
He's not heavy, he's my brother.
TIPS
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L.G.L.
S(t) = 0.29(t 1990)2 + 21Set S(t) to 50, and "solve" for t!
0.29(t 1990)2 + 21
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Unit TestThe Day After Tomorrow
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Think, Pair, ShareIn how many ways can a line intersect a parabola?
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Think, Pair, ShareHow many times can a line intersect a parabola?
NeverOnceTwice
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LinearQuadratic Systems
A line can intersect a parabola in 3 different ways:
1. Two points of intersection.
2. One point of intersection.
(the line is said to run "tangent" to the parabola)3. No points of intersection.
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Think, Pair, ShareHow can we determine whether a line and a parabola meet once, twice or never without actually solving (or graphing)?
Look at the discriminant!
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To find the yvalues of the points of intersection, take the xvalues that we found using the quadratic formula and plug them in to the equation.
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Return to Profit Models
Revenue Function
Profit Function
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Above we see the Cost Function and the Revenue Function
What will the Profit Function look like?
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Skeet shooting
They meet when the height of the ball is THE SAME as the height of the paintball.
ORRRRRR when h(t) = g(t)
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Skeet shooting
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Our Good Friend k
Determine the value(s) of k that such that g(x) = 6x + k intersects f(x) = 4x2 2x 5 at only one point.
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Our Good Friend kDetermine the value(s) of k that such that g(x) = 2x + k does not intersect f(x) = 3x2 + 4x + 1.
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Clear / Unclear
LinearQuadratic Systems
Solving by FactoringSolving by the Quadratic Formula
RadicalsProfit Functions
Determining an Equation from Given Information
Determining the Inverse of a Quadratic
Completing the Square
Determining features from a graphDetermining features from an equation