1 / 30

Chapter 5 Prentice Hall

Chapter 5 Prentice Hall. Quadratics. 5.1/5.2 Graphing quadratic functions. Quadratic function : f(x) = ax ² + bx + c Graph is a parabola. Quadratic Term. Constant Term. Linear Term. ax ² + bx + c. y-intercept is c Where x=0 Equation of the axis of symmetry:

pennie
Download Presentation

Chapter 5 Prentice Hall

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 5 Prentice Hall Quadratics

  2. 5.1/5.2 Graphing quadratic functions • Quadratic function: f(x) = ax² + bx + c • Graph is a parabola Quadratic Term Constant Term Linear Term

  3. ax² + bx + c • y-intercept is c Where x=0 • Equation of the axis of symmetry: • x-coordinate of the vertex:

  4. Example • Consider f(x) = x² + 9 + 8x • Find the y-intercept, equation of the axis of symmetry and the x-coordinate of the vertex. • A=1, B= 8 and C=9 • Y int = 9 • X=-b/2a • X=-4

  5. Maximum or Minimum • a>0: opens up/minimum • a<0: opens down/maximum • f(-b/2a) is value of max or min

  6. Maximum or Minimum • Max or Min can be found at the y coordinate of the vertex. • How do we find the x coordinate? • -b/2a • Then plug in x value to find y value.

  7. 5.3 Movement of Graphs • Graph f(x) = x2 and g(x) = -x2. Describe how the graphs of f(x) and g(x) and are related.

  8. Change to Parent Graph Reflections Y=-f(x) Outside the HVertical Axis Reflected over the x-axis Y=f(-x) Inside the HHorizontal Axis Reflected over the y-axis

  9. Change to Parent Graph Translations +,- OUTSIDE of Function Outside the H Vertical Movement SHIFTS UP AND DOWN +,- INSIDE of Function Inside the H Horizontal Movement SHIFTS LEFT AND RIGHT

  10. Change to Parent Graph Dilations X/÷ OUTSIDE of Function Outside the H Vertical Movement Expands/Compresses X/÷ INSIDE of Function Inside the H Horizontal Movement Expands/Compresses

  11. Examples - Use the parent graph y = x2 to sketch the graph of each function. • y = x2 + 1 • This function is of the form y= f(x) + 1. • Outside the HVertical Movement • Since 1 is added to the parent function y = x2,the graph of the parent function moves up 1 unit.

  12. Examples - Use the parent graph y = x2 to sketch the graph of each function. • y = (x - 2)2 • Inside the HHorizontal Movement • This function is of the form y = f(x - 2). • Since 2 is being subtracted from x before being evaluated by the parent function, the graph of the parent function y = x2 slides 2 units right. a.

  13. Examples - Use the parent graph y = x2 to sketch the graph of each function. • y = (x + 1)2 – 2 • This function is of the form y = f(x + 1)2 -2. The addition of 1 indicates a slide 1 unit left, and the subtraction of 2 moves the parent function y = x2 down two units. a.

  14. 5.5 Solving QE by Graphing • Roots/Zeros • Solutions of the QE • X-Intercepts • Where y=0 • Can check answers if polynomial = 0

  15. Graphing EQUATIONS

  16. Estimating Roots • Solve –x2+4x-1=0 by graphing. If exact roots can not be found, state the consecutive integers between which the roots are located • X Intercepts are where? • Between 0 and 1 and between 3 and 4

  17. 5.4 Solve QE by factoring • Zero product property – if ab = 0, then a = 0, b = 0, or both This means to factor and set each equal to zero

  18. To write an equation given roots • 1. Use (x – p)(x – q) = 0 • 2. FOIL or BOX • 3. Multiply to ensure a,b,c are integers

  19. 5.7 Completing the square • Square root property: If x² = n , then x2+10x+25=49 X2-6x+9=32

  20. CTS: put in form ax² + bx = c Find: • b = • ½ b = • (½b)² = • Add (½b)² to both sides • Re-write LHS as a perfect square • Solve • x2+bx+(b/2) 2=(x+b/2) 2

  21. When should I CTS? • You can only CTS when a = 1 • Only complete the square if b is even • x2+4x-12=0 • 3x2-2x-1=0 • x2+2x+3=0

  22. Vertex Form: y = a(x – h)² + k • Vertex: (h, k) • Axis of sym: x = h • a means: open up/down and wide/narrow

  23. Convert from quadratic form to vertex form • 1. Isolate y • 2. Complete the square on the RHS • 3. Add/subtract same # on the right • (if a ≠ 1, start by factoring a out of first two terms) • Check to see if both are same parabola in calculator

  24. To write in vertex form given vertex and a point: • 1. Use x, y, h, k to find a • 2. Plug in values of h, k, a into vertex form • Check mult. Choice by graphing and checking table

  25. 5.8 Quadratic Formula • If • Then

  26. Discriminant • If

  27. QUADRATIC EQUATIONS • b2-4ac >0 • Two distinct real roots • b2-4ac=0 • Exactly one real root (actually a double root) • b2-4ac<0 • No real roots (Two distinct imaginary roots)

  28. To graph quadratic inequalities • 1. Graph parabola • 2. Test a point inside • 3. True: shade inside False: shade outside

  29. To solve quadratic inequalities algebraically • 1. Find zeros • 2. Test points left, center, and right

  30. Number Theory • Find two real numbers whose sum is 6 and whose product is 10 or show that no such numbers exist • X=One number • 6-x=the other number • Product is 10 • X(6-X)=10 • Solve by graphing/factoring • No such numbers

More Related