Quad fcn

525 views

Published on

quadratic function lesson using doceri

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
525
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
6
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide
  • Sports objects often follow these paths. Polynomial whose largest exponent is 2. SLO – use graphs of quadratics to gain geometric understanding of the algebra that appears in football, baseball, basketball, etc. Refer to general form
  • Symmetry! Vertex. Opens up or down depending on sign of a
  • Vertex form with tranformations
  • Will the vertex be a max or a min?
  • (5,0), (1,0), (0,-10)
  • What’s different? Vertex & solving for x-intercepts.
  • Quad fcn

    1. 1. Quadratic FunctionsGraphing and Modeling
    2. 2. Quadratic Functions as Projectilesf (x)= ax2+bx+c where a, b and c are real and a ¹ 0.
    3. 3. Characteristicsof Graphs
    4. 4. Relating Solutions of the QuadraticEquation with x-intercepts
    5. 5. Relating Graphs with theQuadratic Formula
    6. 6. The Basic Quadratic and theTransformed Quadratic
    7. 7. Graphing Quadratic Functionin Vertex Form – The StepsDetermine whether theparabola opens UP orDOWNDetermine the vertex(h,k)Find any x-interceptsby solving f(x)=0Find the y-interceptby computing f(0)Plot the interceptsand vertexf (x) = a(x -h)2+k
    8. 8. Graphing Quadratic Functionin Vertex Form – An Examplef (x) = -2(x -3)2+8a = -2 h = 3 k = 8Since a is negativewe know the parabolaopens DOWNSince the vertex hasthe form (h, k), ourvertex will be (3, 8)
    9. 9. Graphing Quadratic Function inVertex Form – An ExampleSolving for the x- and y-intercepts
    10. 10. Graphing Quadratic Function inVertex Form – An Example
    11. 11. Graphing Quadratic Functionin General Form – The StepsDetermine whether theparabola opens UP orDOWNDetermine the vertexFind any x-interceptsby solving f(x)=0Find the y-interceptby computing f(0)Plot the interceptsand vertexf (x) = ax2+bx+c-b2a, f -b2aæèçöø÷æèçöø÷
    12. 12. Graphing Quadratic Function inGeneral Form – An Examplef (x) = x2+4x+1a =1b = 4Since a is positivewe know theparabola opens UPx-coordinateof the vertex:y-coordinateof the vertex:The vertex:-2,-3( )
    13. 13. Graphing Quadratic Function inGeneral Form – An ExampleSolving for the x- and y-intercepts
    14. 14. Graphing Quadratic Function inGeneral Form – An Example
    15. 15. The Parabolic Path of aPunted FootballWhen a football is kicked, the height ofthe punted football, f(x), in feet, canbe modeled byf (x)= -0.01x2+1.18x+2where x is the ball’s horizontaldistance, in feet, from the point of impactwith the kicker’s foot.a. What is the maximum height of the punt?x = -b2a= -1.182(-0.01)= -(-59) = 59 feet
    16. 16. The Parabolic Path of aPunted FootballWhen a football is kicked, the height ofthe punted football, f(x), in feet, canbe modeled byf (x)= -0.01x2+1.18x+2where x is the ball’s horizontaldistance, in feet, from the point of impactwith the kicker’s foot.a. What is the maximum height of the punt?f (59)= -0.01(59)2+1.18(59)+2The maximum height of the punt occurs 59 feet from thekicker’s point of impact. The actual maximum height of thepunt is=36.81 feet
    17. 17. The Parabolic Path of a PuntedFootball Continuedf (x)= -0.01x2+1.18x+2b. How far must the nearest defensiveplayer, who is 6 feet from thekicker’s point of impact, reach toblock the punt?This means we need to find the heightof the ball 6 feet from the kicker.In other words, “plug in” 6 for x.f (6)= -0.01(6)2+1.18(6)+2 =8.72 feetThe defensive player must reach 8.72feet above the ground to block the punt.
    18. 18. Key Points to Know for GraphingQuadratic Functions:General form versus Vertex formUnderstanding the shape of a quadraticfunctionWhen a parabola opens up or downUsing either form to graph a parabolaAble to solve for a maximum or minimumAble to solve for x- and y-intercepts
    19. 19. I Challenge You…Write a quadratic function in standardform that models the area of the shadedregion.x +9x+5x +1 x+3x +3x -1xx

    ×