Lect3B - Quadratic Functions f ( x) = a x 2 + b x + c...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
92.131 Lecture 3B 1 of 14 Ronald Brent © 2010 All rights reserved. x −4 −3 −2 −1 0 1234 y −4 −3 −2 −1 1 2 3 4 Quadratic Functions c x b x a x f + + = 2 ) ( Graphs of quadratics functions are parabolas opening up if a > 0, and down if a < 0. Examples: x x y 4 2 2 = 2 2 x y = 2 2 2 + = x x y 2 x y =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
92.131 Lecture 3B 2 of 14 Ronald Brent © 2010 All rights reserved. Notes: 1) Quadratic functions always have an axis of symmetry, that is a vertical line about which the graph is symmetric. This line is a b x 2 = 2) They also have a point where they “turn around”. This point is called the vertex and it occurs where a b x 2 = , and a b c y 4 2 = . 3) They may or may not intersect the x –axis. This depends upon the discriminant, c a b 4 2 . How to graph a quadratic function c x b x a x f + + = 2 ) ( 1) Determine the vertex by first computing a b 2 . 2) Find the y -intercept. (Set x = 0.) 3) Determine x -intercepts by solving 0 2 = + + c x b x a .
Background image of page 2
92.131 Lecture 3B 3 of 14 Ronald Brent © 2010 All rights reserved. x - 5 - 4 - 3 - 2 - 1 12345 -5 -4 -3 -2 -1 0 1 2 3 4 y 5 Example: Graph 3 4 ) ( 2 + = x x x f . Here a = 1, b = 4, and c = 3, so 2 2 4 2 = = a b . Since a > 0, the graph is a parabola opening upwards. The vertex is when x = 2, in which case y = 1. So, it is the point (2, 1). The y -intercept is (0, 3). The x -intercepts occur where 0 3 4 2 = + x x , or x = 1, and x = 3. Now one can graph: (0, 3) (2, 1) (3, 0 ) (1, 0 )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
92.131 Lecture 3B 4 of 14 Ronald Brent © 2010 All rights reserved. Scaling Functions Vertical Scaling: Suppose k > 0, then one may obtain the graph of ) ( x f k y = by stretching the graph vertically of ) ( x f y = if k > 1, or compressing the graph (vertically) of ) ( x f y = if 0 < k < 1 .
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 14

Lect3B - Quadratic Functions f ( x) = a x 2 + b x + c...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online