pahlevanlu

Exploring Quadratic Functions

katiat2016

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 U-shaped curved line known as a parabola which can open facing upwards or downwards and the width and steepness of the U shape can vary.
  1. Give an example of a quadratic function and give an example of a function that is NOT a quadratic.
  • Quadratic Function: y= 2x2 + 3x + 5
  • Not a quadratic Function: y = 2x + 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.
  • The lines on both sides of the y axis are identical but just curved opposite ways
  1. Keep b = c = 0. Change the value of :
      1. Does the graph open up or open down?
  • The graph opens downwards
    1. Does the graph have a maximum point or minimum point?
  • The graph does not have a maximum point it continues on forever
      1. Does the graph open up or open down?
  • The graph curves and opens upwards
    1. Does the graph have a maximum point or minimum point?
  • No, the graph doesn’t have a max or min point it doesn’t end
      1. Is the graph narrow or wide?
  • The graph is much wider
      1. Is the graph narrow or wide
  • The graph is 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. The point where the graph begins changes and moves up and down based on what number you change c to.

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 = 8x2+ x + 0 = y = 8x2

 

This quadratic equation has ONE solution.

 

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

 

Equation: y=-2.8x2+-2.8x

 

This quadratic equation has TWO solutions.

 

Adjust the sliders so that the curve does NOT cross the x-axis. You just move c to put the curve above the center point

 

Equation:  y = 10x2+ x + 0.5

 

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