1. Definitions
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Quadratic Equation in standard form is viewed as, ax2 + bx + c = 0, where a ≠ 0
Parabola is a u-shaped graph
If a is positive, it opens up
If a is negative, it opens down
Vertex is the highest or lowest point of the graph
Axis of Symmetry is the vertical line passing through the vertex (the “x” of vertex) it is represented by a DASHED-line
Roots/Zeros are the solutions to the Quadratic it is where the graph crosses the x-axis.
Also known as the minimum or maximum value

2. Definitions
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y = x2 – 4
Roots: The solutions to the equation . Also known as the zeros
X-intercept(s): Point(s) where the graph crosses the x-axis.
Ordered Pair: (–2, 0)
Ordered Pair: (2, 0)
Vertex: Minimum or maximum value
Axis of Symmetry: Line that separates the graph in half; always written as
x = ______

3. To graph a Quadratic Equation
1st find the Vertex
a. find the x-coordinate of the vertex by using the vertex formula.
b. Substitute the x-value into the Quadratic equation to find the y-value of the vertex.
Write the vertex as an ordered pair. (x, y)
The x-value of the vertex ALSO gives the Axis of Symmetry.
Write the Axis of Symmetry as an equation. x =__

4. 2nd find the Roots…when y=0.
***where the graph crosses the x-axis*** a.
Set the equation = to 0 b.
Factor the equation. c.
Solve each factor for x.

5. Example 1 Given equation: Find the vertex The x-value of vertex is:
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Given equation:
Find the vertex
The x-value of vertex is:
The y-value of vertex:
Vertex:
Axis of symmetry:
Minimum/maximum:

6. Example 1 Find the Roots Set the equation = 0 Factor the equation
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Find the Roots
Set the equation = 0
Factor the equation
Solve for x
Roots:

7. Example 1 Vertex: Axis of symmetry: Roots: What is the Domain?
Is the vertex a minimum or maximum point?
Minimum at y = –9
Vertex:
y-intercept:
Axis of symmetry:
Roots:
Reflection over axis of symmetry
No reflection
What is the Domain?
What is the Range?

8. Example 2 Given equation: vertex y-coordinate Axis of symmetry
Roots (y=0)
1 solution
Min/max?
Min at y = 0
Find the y-intercept (x=0)
Domain
Reflection over axis of symmetry
Range 8

9. Example 3 Given equation: vertex y-coordinate Axis of symmetry
y-intercept:
Given equation:
Reflection over axis of symmetry
vertex
No reflection
y-coordinate
Axis of symmetry
Roots (y=0)
Min/max?
Min at y = -2
Domain
Range

10. Your turn Given equation, y = 2x2 – 2x + 5 Determine: up How it opens
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Given equation, y = 2x2 – 2x + 5
Determine:
How it opens
Y-Intercept
The Vertex
Axis of Symmetry
Domain
Range
Minimum/Maximum up
(0, 5)
(0.5, 4.5)
x = 0.5
All Real Numbers
y > 4.5
No solution
Min at 4.5