Functions and Quadratic Equations

Functions and Quadratic Equations

1. Quadratic Functions and Their Properties

   • A quadratic function is the function of the form:
   • It's general properties are:
     • A CANNOT equal 0
     • Parabola opens up if A is bigger than 0.
     • Parabola opens down if A is smaller than 0.

2. Graph a Quadratic Function Using Transformations

   • The standard form is useful for determining how the graph is transformed from the graph of y=x^2, which means that if something is added to the x^2, it's going to change how the graph is represented.

3. Identify the Vertex and Axis of Symmetry of a Quadratic Function

   • The ways of finding the answer can vary depending on whether we're trying to find the vertex or the axis of symmetry.
     • The Vertex
       • To find the vertex, we have to use the equation: (-B/2A, f(-B/2A)).
     • The Axis of Symmetry
       • The axis of symmetry of a parabola can be determined by the expression x = x^1 + x^2/2, where x^1 and x^2 are the roots of the quadratic function.

4. Find a Quadratic Function Given Its Vertex and One Other Point

   • The vertex is always the maximum or minimum value when it comes to quadratic equations, so it's a pretty good place to start.
     • The other point would probably be the intercepts, also known as the C coefficient, because as it is completely symmetrical, we could be able to find the axis.

5. Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts

   • We need to do different equations depending on what we're trying to find, in this case the vertex, the axis, and the intercepts
     • The Vertex
       • As I already explained, to find the vertex of a quadratic function, we have to use the equation: (-B/2A, f(-B/2A)).
     • The Axis
       • As I too, already explained before, to find the axis of symmetry of a parabola we have to use the equation x = x^1 + x^2/2, where x^1 and x^2 are the roots of the quadratic function.
     • The Intercepts
       • In the quadratic function, Ax^2 + Bx + C, the coefficient C is always where the parabola intercepts the axis Y.

6. Find the Maximum or Minimum Value of a Quadratic Function

   • In the specific case of a quadratic function, the maximum or minimum of a parabola will always be the vertex, as it is where the parabola always begins, whether the arms are going up or down.

7. Made by:

   • Marah Escobar Mathews

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