The Graph of f ( x ) = ax 2

1 / 18

# The Graph of f ( x ) = ax 2 - PowerPoint PPT Presentation

The Graph of f ( x ) = ax 2.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' The Graph of f ( x ) = ax 2' - reegan

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

The Graph of f (x) = ax2

All quadratic functions have graphs similar to y = x2. Such curves are called parabolas. They are U-shaped and symmetric with respect to a vertical line known as the parabola’s axis of symmetry. For the graph of f (x) = x2, the y-axis is the axis of symmetry. The point (0, 0) is known as the vertex of this parabola.

6

5

4

3

2

1

The Graph of f (x) = a(x – h)2

We could next consider graphs of f(x) = ax2 + bx + c, where b and c are not both 0. It turns out to be convenient to first graph f(x) = a(x – h)2, where h is some constant. This allows us to observe similarities to the graphs drawn in previous slides.

Graphing f (x) = a(x – h)2 + k

The graph of f (x) = a(x – h)2 + k has the same shape

as the graph of y = a(x – h)2.

If kis positive, the graph of y = a(x – h)2is

shifted k units up.

If kis negative, the graph of y = a(x – h)2is

shifted |k| units down.

The vertex is (h, k), and the axis of symmetry is x = h.

The domain of f is (,).

If a> 0, the range is f is [k,). A minimum function value is k, which occurs when x = h.

For a< 0, the range of f is (, k]. A maximum function value of koccurs when x = h.