Problem 1 Graphing a Function of the Form f ( x ) = a x 2 f open x close equals eh , x squared

What is the graph of f ( x ) = 1 2 x 2 ? f open x close equals , 1 half , x squared , question mark

• Step 1 Plot the vertex (0, 0). Draw the axis of symmetry, x = 0.

• Step 2 Find and plot two points on one side of the axis of symmetry.

  x	f ( x ) = 1 2 x 2 f open x close equals , 1 half , x squared	(x, f(x))
  0	1 2 ( 0 ) 2 = 0 1 half , open 0 , close squared , equals 0	(0, 0)
  2	1 2 ( 2 ) 2 = 2 1 half , open 2 , close squared , equals 2	(2, 2)
  4	1 2 ( 4 ) 2 = 8 1 half , open 4 , close squared , equals 8	(4, 8)

• Step 3 Plot the corresponding points on the other side of the axis of symmetry.
• Step 4 Sketch the curve.

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✓ Got It?

1. 1. What is the graph of f ( x ) = − 1 3 x 2 ? f open x close equals negative , 1 third , x squared , question mark
   2. Reasoning What can you say about the graph of the function f ( x ) = a x 2 f open x close equals eh , x squared  if a is a negative number? Explain.

Take Note Key Concept: Reflection, Stretch, and Compression

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Reflection, a and − a negative eh

Stretch, a > 1 eh greater than 1

Compression, 0 < a < 1 0 less than eh less than 1

If a > 0 , eh greater than 0 comma  the parabola opens upward. The y-coordinate of the vertex is the minimum value of the function. If a < 0 , eh less than 0 comma  the parabola opens downward. The y-coordinate of the vertex is the maximum value of the function.