CLASS 10 · LEARNING KNOWLEDGE
Quadratic Models and Extremes
How it works
The vertex form shows the largest or smallest function value of a parabola. For a<0 the vertex is a maximum, for a>0 a minimum. In real-world contexts, units and permissible value ranges must be considered.
Note
f(x)=a(x−h)²+k; Extremum k at x=h.
f(x)=a(x−h)²+k; Extremum k at x=h.
An example
A throwing height is modeled by h(t) = −4(t−7)² + 80. What is the maximum height? Give the result in m.
The quadratic term is never positive. At t=7 it is zero; maximum=80. Result: 80 m.
Try it yourself now
50 Exercises · three difficulty levels · selection and number input
To the learning unit →Own explanation and own practice exercises by AmyMath. Subject reference framework: KMK Educational Standards Mathematics ESA/MSA. The topic assignment may vary by federal state.