Download presentation

Presentation is loading. Please wait.

1
Quadratic Functions

2
**p(x) = an xn + an-1 xn-1 + … + a1 x + a0**

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

3
**Quadratic functions Definition: p(x) = ax2 + bx + c**

A polynomial of degree 0 is called a constant function. A polynomial of degree 1 is called a linear function. Definition: A degree 2 polynomial 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. Quadratic functions are incredibly important functions that show up everywhere in the real world.

4
**Parabolas p(x) = ax2 + bx + c a > 0 a < 0**

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 a decreases from 1 towards 0**

How does the graph of a quadratic function change as we change a, b, and c? a decreases from 1 towards 0

6
**Parabolas a increases from 1 to 10**

How does the graph of a quadratic function change as we change a, b, and c? a increases from 1 to 10

7
**Parabolas c increases from 0 to 2**

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

8
**Parabolas c decreases from 0 to -2**

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

9
**Standard form Definition: p(x) = a(x – h)2 + k**

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.

10
**Summary General Form: standard Form: Vertex: Axis of symmetry: Vertex:**

Parabola opens up Parabola opens down

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

12
problems Find the quadratic function with 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) = x – 0.5x2 How much should the company spend on advertising to maximize profits?

Similar presentations

OK

Vocabulary of a Quadratic Function Vacation… November 30, 2015.

Vocabulary of a Quadratic Function Vacation… November 30, 2015.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on indian railway reservation system Ppt on tcp/ip protocol suite by forouzan Ppt on love marriage in india Ppt on national stock exchange in india Ppt on kingdom monera bacteria Ppt on meaning of economics Ppt on supply chain management of mcdonald Ppt on applied operations research va Ppt on schottky diode model Ppt on arunachal pradesh cultured