Quadratic Function Assignment

Exploring quadratic functions (7.1)

Follow the instructions laid out in this worksheet and post your answers in a blog post. Use www.desmos.com to answer the questions below.
Due: Wednesday Sept 26th
Title: Exploring quadratic functions
Categorize: Math 11
Tag: quadratics, pahlevanlu

  1. Find and write the definition of a quadratic function in words you understand. (use your textbook, google, etc)

A quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in width or steepness, but they all have the same basic “U” shape.

  1. Give an example of a quadratic function and give an example of a function that is NOT a quadratic.

This IS a quadratic function : y=2x^2+3x+8

This IS NOT a quadratic function : Y=4x+5

  1. Go to desmos.com and type in the following function:
    1. Desmos will give you the option of adding “sliders” for or all. Click all. This will allow you to change the values of  to see how the graph changes.
    2. Start with slider values . Describe any symmetry you notice.

They are identical on both sides of the Y axis.

  1. Keep b = c = 0. Change the value of :
      1. Does the graph open up or open down?

It faces downwards

  1. Does the graph have a maximum point or minimum point?

no

    1. Does the graph open up or open down?

The graph faces upwards

  1. Does the graph have a maximum point or minimum point?

no

    1. Is the graph narrow or wide?

Wide

    1. Is the graph narrow or wide

Narrow

  1. We call the maximum or minimum point of a quadratic function the vertex. Complete the following statements:
    1. When is Positive the vertex is a minimum
    2. When is Negative, the vertex is a maximum
  2. Let and Use the slider to change the value of Describe how the graph changes as changes.

When you move C to a bigger number the quadratic function moves up in the graph and the opposite happens when you drop the number.

Roots are the solutions to the quadratic equation.  The roots are found by looking at where the curve crosses the x axis (x-intercepts).

Adjust the sliders for a, b and c so you can get a curve that just touches the x axis (y=0).

 

Equation: Y=10x^2

 

This quadratic equation has ONE solution.

 

Adjust the sliders so you can get the roots of 0 and -1

 

Equation: y=-2.8x^2+-2.8x

 

This quadratic equation has TWO solutions.

 

Adjust the sliders so that the curve does NOT cross the x-axis.

 

Equation:  Y=10x^2+x+0.5

 

When the curve does NOT cross the x-axis, there are NO REAL solutions for this equation.

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