# Unit Four - Quadratic Relations Lesson 1 - Properties of Quadratics ```Unit Four - Quadratic Relations
Lesson 1 - Properties of Quadratics
Learning Goals:
- be able to state the properties of a parabola
- be able to recognize a quadratic based on the graph,
equation, or table of values
- use the standard form of an equation to find properties
of the parabola
Let's Review...The Parabola
opens down
opens up
Tables of Values
Standard Form
Opens down if a is negative.
Opens up if a is positive.
The Parabola
Standard Form - Finding the Axis of Symmetry
The axis of symmetry is a horizontal line.
It has the equation, x = a, for some value a where the axis of
symmetry would cross the x-axis.
For an equation ax2+bx+c, the equation of the axis of symmetry
is given by
Example 1. What is the axis of symmetry of 2x2-3x+6?
The vertex is on the axis of symmetry.
Finding the vertex of a quadratic in standard form...
Step 1)
The axis of symmetry is given by x = a.
Substitute the &quot;a&quot; into the equation for x.
Step 2)
Calculate the value for a subbed in for x.
Step 3)
The x-co-ordinate of the vertex is given by a.
The y-co-ordinate of the vertex is given by the
value that you get in Step 2).
Example 2. Find the axis of symmetry and the vertex for the
parabola below.
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