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EXAMPLE 1 Graph a function of the form y = ax 2 Graph y = 2x 2. Compare the graph with the graph of y = x 2. SOLUTION STEP 1 Make a table of values for.

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Presentation on theme: "EXAMPLE 1 Graph a function of the form y = ax 2 Graph y = 2x 2. Compare the graph with the graph of y = x 2. SOLUTION STEP 1 Make a table of values for."— Presentation transcript:

1 EXAMPLE 1 Graph a function of the form y = ax 2 Graph y = 2x 2. Compare the graph with the graph of y = x 2. SOLUTION STEP 1 Make a table of values for y = 2x 2. STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points.

2 EXAMPLE 1 Graph a function of the form y = ax 2 STEP 4 Compare the graphs of y = 2x 2 and y = x 2. Both open up and have the same vertex and axis of symmetry. The graph of y = 2x 2 is narrower than the graph of y = x 2.

3 EXAMPLE 2 Graph a function of the form y = ax 2 + c Graph y = – Compare the graph with the x 2 + 3 1212 graph of y = x 2 SOLUTION STEP 1 Make a table of values for y = – x 2 + 3 1212 STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points.

4 EXAMPLE 2 Graph a function of the form y = ax 2 STEP 4 Compare the graphs of y = – and y = x 2. Both graphs have the same axis of symmetry. However, the graph of y = – opens down and is wider than the graph of y = x 2. Also, its vertex is 3 units higher. x 2 + 3 1212 1212

5 GUIDED PRACTICE for Examples 1 and 2 Graph the function. Compare the graph with the graph of y = x 2. 1. y = – 4x 2 SOLUTION STEP 1 Make a table of values for y = – 4x 2. X – 2 – 102 Y – 16 – 40 – 16 – 4

6 GUIDED PRACTICE for Examples 1 and 2 STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points. STEP 4Compare the graphs of y = – 4x 2 and y = x 2. Same axis of symmetry and vertex, opens down, and is narrower ANSWER

7 GUIDED PRACTICE for Examples 1 and 2 2. y = – x 2 – 5 SOLUTION STEP 1 Make a table of values for y = – x 2 – 5. X – 2 – 102 Y – 9 – 6 – 5 – 9 – 6 STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points. STEP 4Compare the graphs of y = – x 2 – 5 and y = x 2.

8 GUIDED PRACTICE for Examples 1 and 2 ANSWER Same axis of symmetry, vertex is shifted down 5 units, and opens down

9 GUIDED PRACTICE for Examples 1 and 2 3. f(x) = SOLUTION STEP 1 X – 4 – 20 – 4 2 Y – 2 4264 STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points. STEP 4 x 2 + 2 1414 Make a table of values for f(x) = x 2 + 2 1414 Compare the graphs of f(x) = and y = x 2. x 2 + 2 1414

10 GUIDED PRACTICE for Examples 1 and 2 ANSWER Same axis of symmetry, vertex is shifted up 2 units, opens up, and is wider

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