Move the sliders and watch how a, b, and c change the parabola. The graph now labels the important points directly, so students can clearly see what changed.
y = ax² + bx + c
y = 1.0x² + 0.0x + 0.0
a controls shape
Positive opens upward. Negative opens downward. Bigger value makes it narrower.
b moves the turn
Changing b shifts the turning point left or right.
c moves height
Changing c moves the graph up or down and changes the y-intercept.
Try changing a first. The graph can smile, become narrow, become wide, or flip upside down.
Controls graph direction and width.
Moves the turning point left or right.
Moves the whole graph up or down.
Live Graph Results
Turning Point: (0.00, 0.00)
Direction: Opens upward
y-intercept: (0.00, 0.00)
x-intercepts: x = 0.00
Basketball path
A thrown ball often forms a parabola-like curve.
Bridge design
Curves similar to parabolas are used in arches and structures.
Game animation
Jumping characters and flying objects often use quadratic curves.