- Nonlinear— A function whose graph is not a straight line; its rate of change is not constant.
- Shape— Parabola (U-shaped or inverted U-shaped curve).
- Standard form— f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.
- Axis of Symmetry— The vertical line that divides the parabola into two mirror-image halves; equation is x = -b/(2a).
- Vertex— The highest or lowest point on the parabola; located at (-b/(2a), f(-b/(2a))).
- y-intercept— The point where the graph crosses the y-axis; found by evaluating f(0) = c.
- Minimum—
○ a is: positive (a > 0)
○ minimum value is: the y-coordinate of the vertex
○ range is: [minimum value, ∞)
- Maximum—
○ a is: negative (a < 0)
○ maximum value is: the y-coordinate of the vertex
○ range is: (-∞, maximum value]
Identify characteristics from the graph.
Left graph:
vertex: (0, -1)
axis of symmetry: x = 0
y-intercept: (0, -1)
Right graph:
vertex: (1, 4)
axis of symmetry: x = 1
y-intercept: (0, 3)
Parent Tip: Review the logic above to help your child master the concept of quadratic functions and their graphs worksheet.
