Lesson 9'3 Graphing Quadratic Functions

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Lesson 9.3Graphing Quadratic Functions
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What is a quadratic function?

• A quadratic function is written in the standard
  form of
• y ax2 bx cwhen a ? 0
• How is this different from a linear equation?

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What does the graph of a quadratic equation look
like?

• A quadratic function when graphed forms a figure
  called a parabola.

• A parabola can open up or down this depends on
  the leading coefficient a from y ax2 bx c
• If a is positive, the parabola will open up.
• If a is negative, the parabola will open down.

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The Anatomy of a Parabola

• The vertex is the lowest/highest point on the
  parabola.
• Parabolas are symmetrical. The line passing
  through the vertex that divides the parabola in
  half is called the axis of symmetry.
• The two symmetric parts are mirror images of each
  other.

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Important Graph Facts

• y ax2 bx c
• The axis of symmetry is a vertical line with the
  equation of x -b
• 2a

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The Anatomy of a Parabola
DONT WRITE THIS IN NOTES

• The vertex is sitting on the axis of symmetry.
• If the axis of symmetry is x -b/2a, then
  the x-coordinate of the vertex must be -b/2a.
• To find the y-coordinate for the vertex we find
  plug in the x-coordinate in the equation and
  solve for y.

x -b 2a
Vertex (-b , ?) 2a
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Graphing a parabola
TAKE NOTES NOW.

• Step 1 Identify a, b, c in the equation.
• Step 2 Determine the axis of symmetry (aka the
  x-coordinate of the vertex) x -b/2a.
• Step 3 Create an (x,y) chart where you put 2 xs
  above b/2a and 2 xs below b/2a.

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Graphing a parabola

• Step 4 Calculate the ys for the xs in your
  chart.
• Step 5 Graph the ordered pairs.
• Step 6 Enjoy your parabola.

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Lets graph

• y x2 4x 1
• a 1, b 4, c -1
• So, lets calculate x -b/2a
• x -4/2(1) -4/2 -2
• This means the vertex is (-2, ?)

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Lets graph y x2 4x 1

• Since x -b/2a -2
• Make your (x,y) chart

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Lets graph y x2 4x 1

• Since x -b/2a -2
• Make your (x,y) chart

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Lets graph y x2 4x 1

• Since x -b/2a -2
• Start plugging in to the equation.

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Lets graph y x2 4x 1
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