riley-mcdonald
Uploaded by
9 SLIDES
195 VUES
90LIKES

Understanding Quadratic Functions in Standard Form

DESCRIPTION

Explore the basics of quadratic functions and their standard form, vertex, roots, and graph characteristics. Learn how to analyze and solve quadratic equations efficiently.

1 / 9

Télécharger la présentation

Understanding Quadratic Functions in Standard Form

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. Quadratic Functions The parent function is given as The graph of a quadratic function is called a parabola. This is the parent graph of all quadratic functions.

  2. Quadratic Functions (-3,9) (3,9) A table of values can be constructed from the graph as given to the right. x y -3 9 -2 4 -1 1 (-2,4) (2,4) 0 0 1 1 2 4 3 9 (1,1) (-1,1) (0,0)

  3. Quadratic Functions All other quadratic functions can be expressed in the form: (-3,9) (3,9) This is called the standard form. The general form is given as: (-2,4) (2,4) (1,1) (-1,1) (0,0)

  4. Quadratic Functions (h,k) In standard form, h k (h,k) identifies the vertex of the parabola.

  5. Quadratic Functions (1,8) In standard form, (5,8) a a affects the direction the parabola opens and how wide or narrow it will open. Since a=2 and it is positive, the parabola opens up and (2,2) (4,2) the y-values are all 2 times larger than on the parent graph. (3,0) 2

  6. Quadratic Functions (3,0) In standard form, a (4,-2) (2,-2) If a is negative, the parabola will open down. Since a=-2 and it is negative, the parabola opens down and - 2 - 2 - 2 (5,-8) (1,-8) - 2 the y-values are all 2 times larger than on the parent graph. - 2 - 2 - 2 - 2 - 2

  7. Quadratic Functions (3,8) The points where the parabola intersects the x-axis are called the Rootsor Zeros of the function. (4,6) (2,6) These roots occur when the y-value is equal to zero. Solving for x we get the values: (5,0) 5 1 (1,0) 1 5 X= X= 1 5 1 1 5 5 1 1 1 5 5 5

  8. Quadratic Functions Example: Graph (5, -2) The vertex is (5, -2) (5, -2) (5, -2) (5, -2) The graph opens upward because 3 is positive. (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) The y-values are multiplied by 3. (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) (5, -2) up 3 (5, -2) (5, -2) Over 1

  9. The zeros of the function can be found by setting y=0. Quadratic Functions Now solve for x. The roots or zeros are: (4.33, 0) and (5.66,0)

More Related