Write Quadratic Equation Given Graph

Write a Quadratic Equation given the Graph

Use the calculator to find the quadratic equation given only the graph of the equation
and at least three points on the graph (either observable or stated).
(Of course, if you can clearly identify the "zeros" of the graph, you can form factors and get the equation.)

If you are given the visual graph of a quadratic equation and you are given (or can identify)
at least 3 points, you can use the Quadratic Regression process to create the equation of the graph.

WRITE a quadratic equation from a graph and given points.

For this example, you are given the graph, one observable zero at x = 2, and two additional points. The task is to write a quadratic equation for this graph.
(In this case, the other zero between 0 and 1 cannot be identified.)

Write the equation of the parabola shown at the right, given that the points (0,2), (-1,9) and (3,5) are on the graph.

1. Think of the given points as creating a small table:

x	-1	0	3
y	9	2	5

2. Open a new Document .
Choose #4 Add Lists & Spreadsheet.
Enter data into list. Title columns at top X and Y.

3. Insert another Document: I
Choose #5 Add Data & Statistics
A scatter plot will appear.
At bottom of screen, click and choose X.
At left of screen, click and choose Y.

4. Choose from
#4 Analyze, # 6 Regression, #4 Show Quadratic.

The graph of the quadratic and the quadratic regression equation for the data will appear.

5. ANSWER: y = 2x² + 5x + 2

Given:

(0,2), (-1,9) and (3,5)

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