Quadratic Vocabulary for Algebra II

By: Julia Ledbetter 3rd period

Vertex

Definition: The point at which the axis of symmetry intersects a parabola.
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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.
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Maximum Value

Definition: The y-coordinate of the vertex of the quadratic function

f(x)=a^2 + bx + c, where a<0

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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.

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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.

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Example: Writing Functions in Vertex Form

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Example: Graph Equations in Vertex Form

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Intercept Form

Definition: y=a(x-r1)(x-r2)


This form is to help you find the roots.

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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)

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Example: Completing the Square

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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.
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Example: Solving with Quadratic Formula

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Root (solution, x-intercept, zero)

Definition: The solutions of a quadratic equation. Also known as solutions, x-intercepts, and zeros.
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