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Comparing Graphs of Quadratic Functions

Learn how to graph quadratic functions of the form y = ax^2 and compare them to the graph of y = x^2. Includes step-by-step instructions and examples.

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Comparing Graphs of Quadratic Functions

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  1. EXAMPLE 1 Graph a function of the form y = ax2 Graphy = 2x2. Compare the graph with the graph ofy = x2. SOLUTION STEP 1 Make a table of values fory = 2x2. 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 = ax2 STEP 4 Compare the graphs of y = 2x2and y = x2. Both open up and have the same vertex and axis of symmetry. The graph of y = 2x2 is narrower than the graph of y = x2.

  3. x2 + 3 x2 + 3 12 12 Make a table of values for y = – EXAMPLE 2 Graph a function of the form y = ax2 + c Graph y = – Compare the graph with the graph of y = x2 SOLUTION STEP 1 STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points.

  4. x2 + 3 x2 + 3 12 12 EXAMPLE 2 Graph a function of the form y = ax2 Compare the graphs of y = – and y = x2. Both graphs have the same axis of symmetry. However, the graph of y = – opens down and is wider than the graph of y = x2. Also, its vertex is 3 units higher. STEP 4

  5. for Examples 1 and 2 GUIDED PRACTICE Graph the function. Compare the graph with the graph of y =x2. 1. y = – 4x2 ANSWER Same axis of symmetry and vertex, opens down, and is narrower

  6. ANSWER Same axis of symmetry, vertex is shifted down 5 units, and opens down for Examples 1 and 2 GUIDED PRACTICE 2. y = – x2 – 5

  7. x2 + 2 14 for Examples 1 and 2 GUIDED PRACTICE 3. f(x)= ANSWER Same axis of symmetry, vertex is shifted up 2 units, opens up, and is wider

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