What you’ll learn
Graph quadratic functions.
Key idea
A parabola changes output by a coefficient times squared distance from its vertex.
Vertex alone does not distinguish V from parabola; two-unit offsets must show squared, not linear growth.
Worked example
Enter the exact value or ordered values in the format requested below.
Full smooth parabolic graph passes through all marked points with V as vertex; x horizontal, y vertical. Read numerical maximum output.
Marked coordinates: V=(-3, 4); L=(-4, 1); R=(-2, 1); L=(-5, -8); R=(-1, -8).
- The smooth parabola has vertex (-3,4) and opens downward, giving maximum output 4.
- One-unit offsets change output by -3, two-unit offsets by -12; y=-3(x+3)²+4 matches quadratic, not linear, distance growth.
Answer: 4
Quick Check
Relate the graph used in 'Graph quadratic functions' to an equation, table, transformation, or verbal description.
Full smooth parabolic graph passes through all marked points with V as vertex; x horizontal, y vertical. Connect to an equation using vertex, opening and two-unit curvature evidence.
Marked coordinates: V=(2, -4); L=(1, -7); R=(3, -7); L=(0, -16); R=(4, -16).