Notes 5.9 Quadratic Applications Quadratic Regressions F L I P V O C A

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Notes 5.9 Quadratic Applications Quadratic Regressions F L I P V O C A B Notes 5.9 Quadratic Applications Quadratic Regressions

Y = 2x2 + x + 3 Quad regression X Y 3 2 13 4 39 F L I P V O C A B Solve systems or complete a quad regression to find the equation containing points f(0)=3, f(2)=13 and f(4)=39 The trick on this slide is recognizing that you were given three coordinates!! They are: X Y 3 2 13 4 39 The quadratic equation is: Y = 2x2 + x + 3

Notes 5.9 F L I P V O C A B A soccer player kicks a ball from the ground. The path of the ball is described by the equation y=-x2+6x where y is height in ft. of the ball after x sec. A. What is the vertex of the parabola? B. What is the maximum height of the ball? C. When does the ball reach the highest point? D. At what second will the ball land on the ground? E. At 2 seconds, how high is the ball?

Notes 5.9 F L I P V O C A B A right triangle has dimensions in inches of x+3, x+10, and x+11 where x is positive. A. Draw and label this information. B. Write an equation to represent this situation. C. Solve the equation and find which root is not reasonable and why. -6 is not a feasible solution for the situation because it would make a side length negative.

Given the fact that rate times time equals distance: Notes 5.9 F L I P V O C A B Given the fact that rate times time equals distance: A. If Katie travelled at a constant rate of r mph for 2 hours, find her distance travelled. B. If Tom travelled at a constant rate of r+3 mph for 2 hours, find his distance. C. Write an equation showing Katie and Tom starting at the same point with Tom travelling East as Katie travels North. At 2 hours, they are apart. -9 is not a feasible solution for the situation because it would make the rates negative. D. Find the rate and distance each travelled in the 2 hour time span. Katie: r=6mph Tom: r=9 mph d= 12 mi. d= 18 mi

Vertex to Standard Review FOIL Distribute

Review Standard to vertex One method is to find a, h, and k and sub into vertex form of the quadratic equation Find the vertex ( h , k ) Review

Standard to vertex Review 2nd method is to complete the square