IV. Quadratic Functions: 10. Applications of Quadratic Functions

When the quadratic function is expressed in a form of , Find the value of for the constants , and .

When two quadratic equations and have the vertices at the same coordinates, find the value of for two constants and .

Find the range of where increases as increases in the graph of the quadratic equation .

When the graph of the quadratic function is translated by parallel to the -axis, the value of increases as the value of increases if . Find the value of in this case.

When the graph of the quadratic function is translated by parallel to the -axis and by parallel to the -axis, it becomes identical to the graph of the quadratic function . Find the value of .

When the graph of the quadratic function is symmetric about -axis to the graph of , find the value of for the constants , and .

When the graph of the quadratic function intersects -axis at and , and intersects -axis at , find the value of .

The graph of the quadratic function intersects -axis at two points. If one is at , find the coordinates of the other. (note, is a constant)

When the graph of the quadratic function intersects -axis at two different points, find the range of .

In the graph of the quadratic function as shown in the figure below, it intersects -axis at two points and , and intersects -axis at the point . Find the area of .

A quadratic function represented by a parabola with the vertex at , which intersects -axis at , can be expressed as . Find the value of for the constants , and .

When the graph of a quadratic function has the vertex at and passes the point , find -coordinate of the point at which the graph intersects -axis.

When the quadratic function whose graph has the axis of symmetry and passes two points and can be represented as , find the value of for the constants , and .

The graph of a quadratic function with the axis of symmetry passes two points and . Find the coordinates at which the graph intersects -axis.

When is the quadratic function whose graph passes three points , and , find the value of for the constants , and .

The graph of a quadratic function intersects -axis at two points and , and also intersects -axis at the point . Find the value of for the constants , and in this case.