Download presentation

Presentation is loading. Please wait.

Published byConrad Watts Modified over 4 years ago

1
Quadratic Functions Algebra III, Sec. 2.1 Objective You will learn how to sketch and analyze graph of functions.

2
Important Vocabulary Axis – the line of symmetry for a parabola Vertex – the point where the the axis intersects the parabola

3
The Graph of a Quadratic Fn A polynomial function of x with degree n is A quadratic function is

4
The Graph of a Quadratic Fn (cont.) A quadratic function is a polynomial function of _____________ degree. The graph of a quadratic function is a special “U” shaped curve called a _____________. second parabola

5
The Graph of a Quadratic Fn (cont.) If the leading coefficient of a quadratic function is positive, the graph of the function opens ________ and the vertex of the parabola is the ____________ y-value on the graph. up minimum

6
The Graph of a Quadratic Fn (cont.) If the leading coefficient of a quadratic function is negative, the graph of the function opens ________ and the vertex of the parabola is the ____________ y-value on the graph. down maximum

7
The Graph of a Quadratic Fn (cont.) The absolute value of the leading coefficient determines ____________________________________. If |a| is small, __________________________________ _______________________________________________. how wide the parabola opens the parabola opens wider than when |a| is large

8
Example 1 Sketch and compare the graphs of the quadratic functions. a) Reflects over the x-axis Vertical stretch by 3/2

9
Example 1 Sketch and compare the graphs of the quadratic functions. b) Vertical shrink by 5/6

10
Standard Form of a Quadratic Fn The standard form of a quadratic function is ________________________________. The axis of the associated parabola is ___________ and the vertex is ____________. a ≠ 0 x = h (h, k)

11
Standard Form of a Quadratic Fn To write a quadratic function in standard form… Use completing the square add and subtract the square of half the coefficient of x

12
Example 2 Sketch the graph of f(x). Identify the vertex and axis. Write original function. Add & subtract (b/2) 2 within parentheses. Regroup terms. Simplify. Write in standard form.

13
Example 2 Sketch the graph of f(x). Identify the vertex and axis. a = 1 h = 5 k = 0 Vertex: (5, 0) Axis: x = 5

14
Standard Form of a Quadratic Fn To find the x-intercepts of the graph… You must solve the quadratic equation.

15
Example 3 Sketch the graph of f(x). Identify the vertex and x- intercepts. Write original function. Factor -1 out of x terms. Add & subtract (b/2) 2 within parentheses. Regroup terms. Simplify. Write in standard form.

16
Example 3 Sketch the graph of f(x). Identify the vertex and x- intercepts. a = -1 h = -2 k = 25 Vertex: (-2, 25) Axis: x = -2

17
Example 3 Sketch the graph of f(x). Identify the vertex and x- intercepts. Set original function =0. Factor out -1. Factor. Set factors =0. Solve.

18
Example (on your handout) Sketch the graph of f(x). Identify the vertex and x- intercepts. Write original function. Add & subtract (b/2) 2 within parentheses. Regroup terms. Simplify. Write in standard form.

19
Example (on your handout) Sketch the graph of f(x). Identify the vertex and x- intercepts. a = 1 h = -1 k = -9 Vertex: (-1, -9) Axis: x = -1

20
Example (on your handout) Sketch the graph of f(x). Identify the vertex and x- intercepts. Set original function =0. Factor. Set factors =0. Solve.

21
Applications of Quadratic Fns For a quadratic function in the form, the x-coordinate of the vertex is given as ___________ & the y-coordinate of the vertex is given as ________.

22
Example 5 The height y (in feet) of a ball thrown by a child is given by, where x is the horizontal distance (in feet) from where the ball is thrown. How high is the ball when it is at its maximum height? a = - 1/8 b = 1 c = 4 Maximum height = vertex

23
Example (on your handout) Find the vertex of the parabola defined by

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google