1 / 14

2.1 Quadratic Functions

2.1 Quadratic Functions. Completing the square Write Quadratic in Vertex form. Definition of a Polynomial Function. F(x) = a n x n + a n-1 x n-1 + a n-2 x n-2 + .. + a 1 x 1 + a 0 a n , a n-1 ,… are numbers In “x n ” n is the exponents going down in degree.

royce
Download Presentation

2.1 Quadratic Functions

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. 2.1 Quadratic Functions Completing the square Write Quadratic in Vertex form

  2. Definition of a Polynomial Function F(x) = a n x n + a n-1 x n-1 + a n-2 x n-2 + .. + a 1x 1 + a0 an , a n-1,… are numbers In “x n” n is the exponents going down in degree. This would be a polynomial function of x with degree n.

  3. Linear functions are first degreeQuadratic functions are second degree f(x) = ax2 + bx + c Would be a graph of a Parabola A parabola is Axis of symmetry symmetric; “x = h” Where h is from the vertex (h, k) If a > 0, then the parabola opens up If a < 0, then the parabola opens downward

  4. What equation do you think of when you hear Quadratic ?

  5. This equation? Do you remember how to use it?

  6. Standard form of a Quadratic equation f(x) = a(x – h) 2 + k How would you graph the equation f(x) = 2(x + 3) 2 + 1 The vertex has moved off the origin 3 units to the left and 1 unit up. Since a = 2,the parabola opens up and gets skinny. The vertex is at (-3, 1)

  7. f(x) = 2(x + 3) 2 + 1

  8. Finding the vertex when it is not in Standard form f(x) = x 2 + 12x – 9 We need to complete the square to find the standard form Take half of b squared and add and subtract to the function. f(x) = x 2 + 12x + (6)2+ ( -36) – 9 Factor the first three terms, then add the last terms f(x) = (x + 6) 2 – 45 vertex ( - 6, -45)

  9. Find the standard form of f(x) = x 2 + 10x + 8

  10. Write the equation with the vertex ( - 4, 8) and the point (1, 4) Start with the standard equation f(x) = a(x – h) 2 + k from the vertex h = - 4, k = 8 from the point x = 1, f(x) = 4 4 = a(1 – (- 4)) 2 + 8 4 = a(5)2 + 8 4 = 25a + 8 -4 = 25a -4/25 = a Rewrite with a, h and k f(x) = -4/25 (x +4)2 + 8

  11. Find the vertex from f(x) = ax2 + bx + c To find “h” we use “b” and “a” To find “k” we place h back in the equation.

  12. Lets find the vertex of the equation f(x) = 4x 2 + 3x – 8 Now let h = -⅜ k = 4(- ⅜)2 + 3(⅜) – 8 k = -137/16 Vertex is ( - ⅜, - 137/16)

  13. Homework Page 116 – 117 #3, 11, 17, 19, 25, 31, 45, 59, 63

  14. Homework Page 116 #22, 33, 51, 64, 73, 77, 80, 83, 89, 91, 104

More Related