2.4+Looking+Back+at+Parabolas

__ **Frogs, Fleas and Painted Cube** __ Quadratic functions can help us describe situations in the real world. What does a quadratic function look like in a situation, table, graph, or equation //February 2 2009, Monday//

**Problem 2.4: Looking Back at Parabolas**
The eight equations below were graphed on a calculator using the window settings sshown. The graphs shown below and on the next page are reproduced on Labsheet 2.4.

//y = X^2 y = x(4 - x) y = (x + 3) (x + 3) y = x(x - 4) y = x(x + 4) y = (x + 3) (x - 3) y = (x + 2) (x + 3) y = 2x(x + 4)//

Do Parts A-F for each equation.


 * A. Match the equation to its graph**



You predict the x intercepts from the equation if you see that specific number being added to or being deducted from x. If the number has been added to x then the intercept is going to be a negative integer, if the number is going to be deducted from x then the x intercept is going to be a positive integer. The coordinates for x intercept: (order is from the first graph to the last graph so, from image 1-2) (1,0) (4,0) (-3,0) (4,0) (-4,0) (3,0), (-3,0) (-2,0) (-3,0) (-4,0)
 * B. Label the coordinates of the x-intercepts on the graph. Describe how you can predict the x intercepts from the equation.**

On the image
 * C. Draw the line of symmetry on the graph.**

(Labels are under the purple writing on the image)** The shapes of the graphs are the parabolas obviously, and are fairly shallow curves judging by its steepness, due to the window settings xmin= -5, xmax= 5 ymin = -10, ymax = 10.
 * D. Describe the shape of the graph and label the coordinates of max/min point.

The most important part of the equation is the given dimension of the equation, which can tell you the x intercept and also the y intercept. I have noticed that if that number is positive it will give me a negative x intercept, and if that number is negative the x intercept will be a positive number. You can find the y intercept if you have two dimensions by multiplying the two dimension sides together.
 * E. Tell what features of the graph you predict from the equation.**


 * F. Draw and Label a rectangle whose aris represented by the equation. Then, express the area of the rectagle in expanded form (Labels are on the image).**



Expanded Form: x^2 + 4x .

**Problem 2.4 Follow Up**
If the equation has X.X for e.g.**x(x** + 4)
 * 1. If an equation is written in factored form, how can you tell whether it represents a quadratic function?**

If the equation has x^2. For. e.g. **x^2** + 4x
 * 2. If an equation is written in expanded form, how can you tell whether it represents a quadratic function?**