• If a < 0, the quadratic will open downwards.
• If a > 0, the quadratic will open upwards.
• Vertical Stretch:
  • Increasing the value of a will vertically expand the graph (ie, make the arms move closer together).
  • Decreasing the value of a will vertically compress the graph (ie, make the arms spread out wider).
• c will always be the y-intercept, because this is the value when x = 0.

  To understand this, substitute 0 for x in the general form.
  a(0)² + b(0) + c
  = 0 + 0 + c
  = c

Quadratic General Form Interactive Activity

Adjust the parameter sliders for a, b, and c. Study the effect of the changes on the y-intercept.
Click SHOW VERTEX to see the coordinates of the vertex..Notice:

• that the values of a, b, and c do not provide a clue to vertex location.
• when b = 0, the vertex and the y-intercept are the same point.

Click SHOW x-INTERCEPT(S) to see the value(s) of the x-intercept(s). These will be solutions of functions of the form: ax² + bx + c = 0

Enrichment: Quadratic General to Standard Form Proof

• Domain: xR.
• Range:
  • if a > 0, y > k
  • if a < 0, y < k