M117 Worksheet Section 12.4 Graphing Parabolas. Name_________________

Directions: Show all work on this Activity paper.

The graph of y = ax² + bx + c is called a parabola. In this activity, you will find a systematic way of graphing parabolas.

Graph y = x² by filling in column 2 of the table below and then graphing the points on the graph that follows.

Column 1 Column 2 Column3 Column 4

x	y = x^2 Ordered pair	y = x^2 + 2 Ordered pair	y = x^2 – 1 Ordered pair
-3	y = (-3)^2 = 9 (-3, 9)
-2
-1
0
1
2
3

.

Your graph should look like the graph above.

Now fill in the third column of your table and then graph your ordered pairs on the above graph.

Your graph should now look like this.

Describe how the two graphs are the same and how they are different

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Fill in the last column of the table and then graph your ordered pairs on the above graph.

Your new graph should look like this. ( over)

Describe how the three graphs are the same and how they are different.

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Describe how the graph of y = x² – 6 will look.__________________________________

The vertex of a parabola is the lowest or highest point on the graph. Find the vertex of the three parabolas that you just graphed.

y= x² ______ y = x² + 2_____ y = x² – 1_______

Notice that the graph of all three parabolas are the same size and shape, but that they have been moved up or down on the y axis.

In general the graph of a quadratic equation of the form y = ax² + k is the same as the graph of y = x² but moved up or down units, depending on whether k is positive or negative.

In order to graph y = 2x² on the following graph, fill in the second column of the following table, then plot your points. Notice y = x² is already graphed for you.

x	y = 2x^2 Ordered pair	y = (1/2)x^2 Ordered pair	y = -2x^2 Ordered pair
3	y = 2(3)^2 = 18 (3,18)
-2
-1
0
1
2

Describe how the graphs of y = x² and y = 2x² are the same and how they are different

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Repeat this procedure for the next last columns. Graph y = (1/2)x² and y = -2x² on the graph above.

Your graph should look like this.

In general, the graph of a quadratic equation of the form y = ax² has its vertex at the origin and open upward if a is positive and downward if a is negative. The parabola is narrower than the basic parabola if >1 and wider if < 1.

Every parabola has a line of symmetry( a line that divides the graph in half). The line is called an axis of symmetry. The axis of symmetry for all of the parabolas above is the y axis or the line x = 0.

Graph each of the following parabolas by filling in the following table and then plotting the points on the following graph.

X	Y = ( x – 1)^2 Ordered pair	Y = ( x + 2)^2 Ordered pair
-3
-2
-1
0
1
2

Your graph should look like this.(over)

Find the vertex of each parabola: y = x² _____y = (x – 1)²______ y = ( x + 2)²______

Find the axis of symmetry for each parabola.

y = x² _____y = (x – 1)²______ y = ( x + 2)²______

In general, the graph of a quadratic equation of the form y = (x - h)² is the same as the graph of y = x² but moved to the right h units if h is positive or moved to the left units if h is negative.

Graph y = ( x + 2)² – 2

Name the vertex and the axis of symmetry. _____________________

Your graph should look like this.

The vertex is at (-2,-2) The graph opens upward and the axis of symmetry is x = -2.

Find the vertex and the axis of symmetry, then state whether each of the following parabolas opens upward or downward.

Equation	Vertex	Axis	Upward or downward
y = ( x – 2)^2 – 3	V(2, -3)	X = 2	upward
y = ( x + 1)^2 - 4
y = -(x – 4)^2 + 6
y = -3(x – 5)^2 - 2
y = (x + 2)^2 + 1
y = -3(x – 4)^2 - 5

y = -(x – 4)² + 6 and y = ( x + 2)² + 1 are graphed on next page. Check your vertex, axis and directions of opening.

Graph the following parabola. Name the vertex and axis of symmetry for each parabola.

1. y = -(x + 3)² – 1 2. y = ( x – 2)² + 3

2. y = 2(x + 3)² – 1 4. y = ( x + 3)²