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EXAMPLE 1

Graph y = ax 2 where a > 1. EXAMPLE 1. STEP 1. Make a table of values for y = 3 x 2. STEP 2. Plot the points from the table. Graph y = ax 2 where a > 1. EXAMPLE 1. STEP 3. Draw a smooth curve through the points. STEP 4.

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EXAMPLE 1

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  1. Graph y= ax2 where a > 1 EXAMPLE 1 STEP 1 Make a table of values for y =3x2 STEP 2 Plot the points from the table.

  2. Graph y= ax2 where a > 1 EXAMPLE 1 STEP 3 Draw a smooth curve through the points. STEP 4 Compare the graphs of y = 3x2and y = x2. Both graphs open up and have the same vertex, (0, 0), and axis of symmetry, x = 0. The graph of y = 3x2 is narrower than the graph of y =x2 because the graph of y = 3x2 is a vertical stretch (by a factor of 3) of the graph of y =x2.

  3. Graph y =ax2 where a < 1 – x2. Graph y= Compare the graph with the graph of 1 1 y = x2. 4 4 – x2. Make a table of values for y = EXAMPLE 2 STEP 1

  4. Graph y =ax2 where a < 1 EXAMPLE 2 STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points.

  5. Graph y =ax2 where a < 1 1 1 1 4 4 4 andy =x2. Compare the graphs ofy = 1 – Both graphs have the same vertex (0, 0), and the same axis of symmetry, x = 0. However, the graph of x2. 4 – – x2 x2 is wider than the graph of y =x2 and it opens down. This is because the graph of is a vertical shrink with a reflection in the x-axis of the graph of y =x2. by a factor of y = y = EXAMPLE 2 STEP 4

  6. EXAMPLE 3 Graph y = x2 + c Graph y = x2+ 5. Compare the graph with the graph of y = x2. STEP 1 Make a table of values for y =x2+ 5.

  7. EXAMPLE 3 Graph y = x2 + c STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points.

  8. EXAMPLE 3 Graph y = x2 + c STEP 4 Compare the graphs of y = x2+ 5and y = x2.Both graphs open up and have the same axis of symmetry, x = 0. However, the vertex of the graph of y =x2+ 5,(0, 5), is different than the vertex of the graph of y =x2,(0, 0), because the graph of y =x2 + 5 is a vertical translation (of 5 units up) of the graph of y =x2.

  9. ANSWER for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. Compare thegraph with the graph ofx2. 1. y=–4x2

  10. 2. y = x2 ANSWER 1 3 for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. Compare thegraph with the graph ofx2.

  11. for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. Compare thegraph with the graph ofx2. 3. y =x2 +2 ANSWER

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