# Section 8.6 Quadratic Functions & Graphs  Graphing Parabolas f(x)=ax 2 f(x)=ax 2 +k f(x)=a(x–h) 2 f(x)=a(x–h) 2 +k  Finding the Vertex and Axis of Symmetry.

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Section 8.6 Quadratic Functions & Graphs  Graphing Parabolas f(x)=ax 2 f(x)=ax 2 +k f(x)=a(x–h) 2 f(x)=a(x–h) 2 +k  Finding the Vertex and Axis of Symmetry  Finding Maximums or Minimums 8.61

Definition Let’s make a table of values for f(x) = x 2 Then sketch the basic parabola shape … 8.62

Make a table of values for f(x) = x 2 Then graph it 8.63

Similar Curves  Changing the coefficient of x 2 :  Smaller is wider  Larger is narrower  The vertex remains the same 8.64

Make a table of values for f(x) = -½x 2 Then graph it 8.65

Reflections  The graph of y= -ƒ(x) is the graph of y = ƒ(x) reflected about the x-axis. 8.66

Vertical Translations If ƒ is a function and k is a positive number, then  The graph of y = ƒ(x) + k is identical to the graph of y =ƒ(x) except that it is translated k units upward.  The graph of y = ƒ(x) - k is identical to the graph of y = ƒ(x) except that it is translated k units downward.  Sketch f(x) = x 2 + 3 on the board 8.67

Horizontal Translations If ƒ is a function and h is a positive number,  Then the graph of y = ƒ(x - h) is identical to the graph of y = ƒ(x) except that it is translated h units to the right.  The graph of y = ƒ(x + h) is identical to the graph of y = ƒ(x) except that it is translated h units to the left. 8.68

Graph f(x) = (x – 3) 2 8.69

Graph g(x) = -2(x +4) 2 8.610

8.611

Graph g(x) = (x – 3) 2 – 5 8.612

Finding the Vertex and Axis of Symmetry Answer the following questions about the given equation: a. Does the graph open upward or downward? b. What are the coordinates of the vertex? c. What is the axis of symmetry? d. Is it narrow or wide? Up (5,1) x=5 narrow 8.613

Finding the Vertex and Axis of Symmetry Answer the following questions about the given equation: a. Does the graph open upward or downward? b. What are the coordinates of the vertex? c. What is the axis of symmetry? d. Is it narrow or wide? Down (-4,-3) x=-4 wide 8.614

Maximums & Minimums 8.615

Maximum or Minimum? Vertex and Axis of Symmetry? 8.616

But what if the function is not in the form of f(x) = a(x – h) 2 + k ? 8.617

What Next?  Section 9.1 Section 9.1 Composite Functions  Sections 8.7 - 8.9 may not be covered8.7 8.618

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