Identify and use the different forms of quadratic functions

The  exercise appears under the Algebra I Math Mission. This exercise practices identifying the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola.

Types of Problems
There is one type of problem in this exercise:


 * 1) Chose the form, find the vertex, and determine if the vertex is a maximum or minimum: This problem provides the values of the function $$g(x)$$ in three forms. Students are asked to choose the form that most easily reveals the vertex of the graph, find the vertex, and determine if the vertex is a maximum or minimum. Identify and use the different forms of quadratic functions.PNG

Strategies
Knowledge of the quadratic formula and strength in arithmetic are encouraged to ensure success on this exercise.
 * 1) The vertex of the graph $$y=g(x)$$ is the only point on the graph that is also on the axis of symmetry. The vertex is always either a maximum (if the parabola opens down) or a minimum (if the parabola opens up).
 * 2) The quadratic function $$g(x)$$ is given in three different forms: standard form, factored form, and vertex form.

Real-life Applications

 * 1) Quadratics are used to model acceleration due to gravity and are useful in the inverse square law from physics.