3. Quadratic Functions

Quadratic Functions Grapher

Manipulate quadratic coefficients (a, b, c) and watch the parabola shift. Compute discriminant (D) and find root intersections on a real-time grid.

Virtual Viewport
Discriminant (D = b² - 4ac) = 16.0 | Real Roots: 2 Distinct

Active Sliders

aCoefficient a1.00scale
-33

Controls curvature and reflection (opens up or down).

bCoefficient b-2.00scale
-55

Shifts the parabola horizontally and vertically.

cConstant c-3.00y-int
-55

Y-intercept of the function (point where x = 0).

Syllabus Objectives

  • Explain the impact of quadratic coefficients on parabola shape
  • Calculate discriminant (b² - 4ac) to determine root quantities
  • Find parabola vertex and root coordinates.

Mathematical Equations

Standard Form
y = a x² + b x + c
Discriminant Formula
D = b² - 4 a c
Quadratic Formula
x = \frac{-b ± √b² - 4 a c}{2 a}

Inquiry Guide Sheet

1

Set a = 1, b = -2, c = -3. Read the roots on graph (-1 and 3). Compute the discriminant.

2

Vary coefficient 'a' from positive to negative. Observe how the parabola flips upside down.

3

Find a combination of a, b, c where discriminant is negative. Verify that the curve has no real roots.