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Quadratic Functions: Standard Form. Today’s Objective: I can graph a quadratic function in standard form. The function models the height h of the soccer ball as it travels distance x . What is the maximum height of the ball? Explain. Quadratic Function: Vertex Form. Attributes:

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quadratic functions standard form

Quadratic Functions:Standard Form

Today’s Objective:

I can graph a quadratic function in standard form

slide2

The function models the height h of the soccer ball as it travels distance x. What is the maximum height of the ball? Explain.

quadratic function vertex form
Quadratic Function: Vertex Form
  • Attributes:
  • Opens up (a > 0) or down (a < 0)
  • Vertex is maximum or minimum
  • Vertex: (h, k)
  • Axis of symmetry:
quadratic function standard form
Quadratic Function: Standard Form
  • Attributes:
  • Opens up (a > 0) or down (a < 0)
  • Vertex is maximum or minimum
  • y-intercept: (0, c)
  • Can be determined with a little work
  • Axis of symmetry:
  • Vertex:
  • (0, c)

Evaluate f(x) at

graphing a quadratic function standard form
Graphing a Quadratic Function: Standard form
  • Vertex:

Plot the vertex

Find and plot two points to the right of vertex.

Plot the pointacross axis of symmetry.

Sketch the curve.

Axis of Symmetry:

Domain:

Range:

All Real Numbers

graphing a quadratic function standard form1
Graphing a Quadratic Function: Standard form
  • Vertex:

Plot the vertex

Find and plot two points to the right of vertex.

Plot the pointacross axis of symmetry.

Sketch the curve.

Axis of Symmetry:

Domain:

Range:

2

All Real Numbers

graphing a quadratic function standard form2
Graphing a Quadratic Function: Standard form
  • Vertex:

Axis of Symmetry:

Domain:

Range:

All Real Numbers

Vertex on Calculator:

[2nd], [trace]

Choose minimum or maximum

Move curser left of vertex, [enter]

Move curser right of vertex, [enter]

[enter]

-0.5

standard form to vertex form
Standard form to Vertex form
  • a value is the same
  • Find the vertex
bungee jumping
Bungee Jumping

You can model the arch of this bridge with the function

How high above the river is the arch?

Maximum

Arch height:

  • Pg. 206 #8-30 evens