1 / 13

Quadratic Functions

Quadratic Functions. Poly Nomials. A polynomial function is a function that can be expressed in the form: p ( x ) = a n x n + a n-1 x n-1 + … + a 1 x + a 0 Where a n , a n-1 , … , a 1 , a 0 are real numbers, a n ≠ 0, the exponents are non-negative integers. Definition :. ✔.

devi
Download Presentation

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. QuadraticFunctions

  2. PolyNomials A polynomial functionis a function that can be expressed in the form: p(x)=an xn + an-1 xn-1 + … + a1x + a0 Where an, an-1 , … , a1, a0are real numbers, an≠ 0, the exponents are non-negative integers Definition: ✔ The degree is 2 ✔ The degree is 1 ✔ The degree is 0 ✔ The degree is 3 The degree of a polynomial is largest exponent of x. Definition:

  3. Quadraticfunctions A polynomial of degree 0 is called a constant function. A polynomial of degree 1 is called a linear function. A degree 2polynomial function is called a quadratic function. The general form a quadratic function is p(x) = ax2 + bx + c where a, b, and c are real numbers with a ≠ 0. Definition: Quadratic functions are incredibly important functions that show up everywhere in the real world.

  4. Parabolas The graph of a quadratic polynomial is called a parabola. p(x)= ax2 + bx + c Axis of Symmetry vertex Axis of Symmetry vertex a > 0 a < 0

  5. Parabolas How does the graph of a quadratic function change as we change a, b, andc? adecreases from 1 towards 0

  6. Parabolas How does the graph of a quadratic function change as we change a, b, andc? a increases from 1 to 10

  7. Parabolas How does the graph of a quadratic function change as we change a, b, andc? c increases from 0 to 2

  8. Parabolas How does the graph of a quadratic function change as we change a, b, andc? c decreases from 0 to -2

  9. Standardform The standard form of a quadratic function is p(x) = a(x – h)2 + k Where (h, k) is the vertex of its graph and a ≠ 0. Definition:

  10. Summary General Form: standard Form: Vertex: Vertex: Axis of symmetry: Axis of symmetry: Parabola opens up Parabola opens down

  11. problems Find the vertex and the x-intercepts of the following functions:

  12. problems Find the quadratic functionwith the indicated vertex that passing though the given point: 1. Vertex: (2,3) Point: (0,2) 2. Vertex: (-2,-2) Point: (-1,0) 3. Vertex: (6,6) Point: (1/2, 3/4)

  13. problems The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) that the company spends on advertising according to the model: P(x) = 230 + 20x – 0.5x2 How much should the company spend on advertising to maximize profits?

More Related