Your SlideShare is downloading. ×
  • Like
Quad fcn
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

Now you can save presentations on your phone or tablet

Available for both IPhone and Android

Text the download link to your phone

Standard text messaging rates apply

Quad fcn

  • 279 views
Published

quadratic function lesson using doceri

quadratic function lesson using doceri

Published in Education , Technology
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
279
On SlideShare
0
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
3
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    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.

Transcript

  • 1. Quadratic FunctionsGraphing and Modeling
  • 2. Quadratic Functions as Projectilesf (x)= ax2+bx+c where a, b and c are real and a ¹ 0.
  • 3. Characteristicsof Graphs
  • 4. Relating Solutions of the QuadraticEquation with x-intercepts
  • 5. Relating Graphs with theQuadratic Formula
  • 6. The Basic Quadratic and theTransformed Quadratic
  • 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. 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. Graphing Quadratic Function inVertex Form – An ExampleSolving for the x- and y-intercepts
  • 10. Graphing Quadratic Function inVertex Form – An Example
  • 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. 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. Graphing Quadratic Function inGeneral Form – An ExampleSolving for the x- and y-intercepts
  • 14. Graphing Quadratic Function inGeneral Form – An Example
  • 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. 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. 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. 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. I Challenge You…Write a quadratic function in standardform that models the area of the shadedregion.x +9x+5x +1 x+3x +3x -1xx