Characteristics of

quadratic functions By Rath Loeung 2 Quadratics are easy to spot.

Look for an x being sqared.

If there is no exponent larger

than a 2, then it's a

quadratic function. y = x + 2x - 4 2 Here's what it looks like graphed Notice its shape.

This U-shape is called a the parent function The parent function of a quadratic

(the function upon which all other quadratics are built) is y = x 2 When x is 0, y is 0

When x is 1, y is 1

When x is 2, y is 4

When x is 3, y is 9

and so on... important characteristics All quadratics have these characteristics.

These can all be figured out using numbers from the function rule. Click on a term or click next. Click next. This is y = x + 2x - 4 2 The vertex is where the graph changes directions.

In this case,

it's changing from decreasing to increasing.

It's going down, down, down and then

right here

it starts going up, up, up. function rule forms There are two forms that a quadratic can be written in. Click on either form or click next. Click next. y = a( x - h) + k 2 vertex form The constants h and k make up the coordinates of

the graph's vertex, which we'll discuss in a little bit.

The vertex point would be (h, k).

Notice that the h is being subtracted in the form.

That means...

A positive h in the form means a negative x coordinate in the vertex.

A negative h in the form means a positive x coordinate in the vertex. oh, and a is not allowed to be zero That would make the function a linear. general form y = ax + bx + c 2 The constants are a, b, and c.

Once again, a cannot be zero because that would

cancel out the x term and make the rule a linear function.

General form is also called "Standard Form." 2 if you have a function in y = x - 2x - 3 2 Use the formula

to find the x-coordinate. Then use that number to plug into x to find the y-coordinate.

Click this circle for an example. y = x - 2x - 3 2 a is 1. b is -2 To find x we use Here's our example. To find y, we plug the 1 back into the x's in the original function rule. The vertex is at

(1, -4) if you have a function in y = (x - 1) - 4 2 h is 1 (remember it's the opposite) and k is -4 The vertex is at (1, -4) Vertices can either be a or a Click next. Finding the line of symmetry is easy... if you've already found the vertex If the vertex is at (2, 10) then the line of symmetry is x = 2.

It's "x equals" whatever the x-coordinate is of the vertex. Click the circle for another example. If the vertex is at (-3, 4)

then the line of symmetry is

x = -3 Finding the y-intercept If x = 0, then you're sitting on the y-axis.

So, in order to find the y-intercept:

Plug a zero into the x's and solve for y

In this example, the y-intercept is -3 y = x - 2x - 3 2 Click next. zeros For a graph, they're called For a function rule, they're called to solve for zeros For now, use your calculators' "calculate zeros"

(2nd calc, zeros).

There are other methods but we won't go into

them here.

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# Characteristics of Quadratic Functions

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