Quadratic Vocabulary for Algebra II
By: Julia Ledbetter 3rd period
Vertex
Definition: The point at which the axis of symmetry intersects a parabola.
Axis of Symmetry
Definition: A line about which a quadratic function (parabola) is symmetric. The equation used to find the axis of symmetry is shown below.
Maximum Value
Definition: The y-coordinate of the vertex of the quadratic function
f(x)=a^2 + bx + c, where a<0
Minimum Value
Definition: The y-coordinate of the vertex of the quadratic function
f(x)=ax^2 + bx + c, where a>0
Standard Form
Definition: A quadratic equation written in the form: ax^2 + bx+ c=0, where a, b, and c are integers, and a cannot = 0
This form is to help you find the y intercept.
Vertex Form
Definition: A quadratic function in the form y= a(x-h)^2 + k, where (h,k) is the vertex of the parabola and x=h is its axis of symmetry.
This form is to help you find the vertex.
Example: Writing Functions in Vertex Form
Example: Graph Equations in Vertex Form
Intercept Form
Definition: y=a(x-r1)(x-r2)
This form is to help you find the roots.
Completing the Square
Definition: All quadratic equations can be solved using the Square Root method Property by manipulating the equation until one side is a perfect square, which is called "completing the square". You are changing the equation from standard form to vertex form.
Follow the Steps below to Complete the Square:
1. Put () around ax^2 + bx
2. Factor the a value from x^2 and x
3. Take 1/2 the middle term and square it
4. Add the number and it's opposite
5. Factor perfect square trinomial
6. Rewrite in the form y= a(x-h)^2 + k (which is vertex form)
Example: Completing the Square
Quadratic Formula
Definition: The solutions of a quadratic equation of the form is ax^2 + bx + c=0, where a cannot equal 0, are given by the Quadratic Formula, which is shown below.
Example: Solving with Quadratic Formula
Root (solution, x-intercept, zero)
Definition: The solutions of a quadratic equation. Also known as solutions, x-intercepts, and zeros.