Quadratic-Functions

Quadratic-Functions - Quadratic Functions Quadratic...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Quadratic Functions Quadratic functions are any functions that may be written in the form y = ax 2 + bx + c where a, b, and c are real coefficients and a 0. For example, y = 2x 2 is a quadratic function since we have the x-squared term. y = x 2 – 1/x + 1 would not be a quadratic function because the 1/x term is equal to x -1 which does not fit the form. The graph of a quadratic function is called a parabola . The Vertex Of The Graph Of A Quadratic Function The vertex of the graph of a quadratic function is defined as the point where the graph changes from increasing to decreasing or changes from decreasing to increasing. Several graphs are shown below along with location of each vertex. Note that the vertex of y=x 2 will be (0,0). Just Remember, The Vertex is the highest or lowest point of the graph. Graphing y=x 2 and Shifts of y=x 2 We can obtain an equation for the graph of any quadratic function we want by applying function graph shift rules to the graph of y=x 2 . For example, if we want a graph that is a vertical stretch of y=x 2 by a factor of two, is shifted right 4 units, and opens downward instead of upward, we use the formula y = -2(x - 4) 2 . The graphs of both are shown below. Note that the vertex has been shifted from (0,0) right 4 units. We use the vertex as our reference point for this new parabola with vertex shifted 4 units right to (4,0).
Background image of page 1

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

View Full DocumentRight Arrow Icon
From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Example: Use function shift rules to predict what the graph of y = 3(x – 4) 2 + 1 will look like. Also, indicate the location of the vertex.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/05/2011 for the course ANTHRO 101 taught by Professor Crandall during the Fall '09 term at BYU.

Page1 / 5

Quadratic-Functions - Quadratic Functions Quadratic...

This preview shows document pages 1 - 3. Sign up to view the full document.

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