The BE WISE Project
H. Atkins
Orientation of the Quadratic Graph
 The standard equation of a quadratic
graph is y = ax2 + bx + c .
 The quadratic graph can be positioned
anywhere on the coordinate plane.
However, while the graph gives its
typical U-shape it can be a ∩-shape as
well.
 the sign on the ax2 will determine if the
graph is a U or a ∩-shape
 U-shape (+ax2 )and ∩-shape (-ax2 )
The BE WISE Project
H. Atkins
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The BE
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The Y- intercept
 The y-intercept of a quadratic graph is
the number where the graph cuts the
y-axis
 This number is evident in the
quadratic equation. The c value in
the standard equation is this number.
 If the equation is y = 2x2 + x – 3 then
the graph will cut the y-axis at -3.
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The BE
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H. Atkins
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X-intercept
 The x-intercept is the number(s) where
the graph cuts the x-axis.
 This number is achieved by finding the
value(s) of x for which y = 0 or
ax2 + bx + c = 0
 Note that it is possible for y = p where p
is a member of the set of real numbers.
In this case the solution will be found
where the graph cuts the line y = p
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The BE
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H. Atkins
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Minimum Value
 The minimum value of a quadratic graph is
the y-value at the lowest point on the graph.
 This value can be calculated using
 When the graph is drawn this value can be
read by drawing a horizontal line through the
bottom of the graph and writing down the
number on the y-axis Through which this line
passes.
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The BE WISE Project
H. Atkins
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Maximum Value
 The maximum value of a quadratic graph is
the y-value at the highest point on the
graph.
 This value can be calculated using
 When the graph is drawn this value can be
read by drawing a horizontal line through
the top of the graph and writing down the
number on the y-axis through which this
line passes.
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The BE
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H. Atkins
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Axis of Symmetry
 The axis of symmetry of a quadratic graph
is an imaginary straight line which divides
the graph into two equal parts.
 If the graph is folded along this line both
halves will exactly match.
 The equation of this line is in the form of
x = k where k is the number on the x-axis
through which the line passes.
 The equation of the axis symmetry can
also be found using
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Minimum Point
 The minimum point of a quadratic
graph is the lowest point on the curve
 The coordinates of this point is
composed of the axis of symmetry and
the minimum value. That is, if the
minimum value is -2 and the axis of
symmetry is x = 3 then the coordinate of
the minimum point is (3,-2).
Maximum
Point
 The maximum point of a quadratic
graph is the highest point of the
curve.
 The coordinates of this point is
composed of the axis of symmetry
and the maximum value. That is, if
the maximum value is 2 and the axis
of symmetry is x = 3 then the
coordinate of the maximum point is
(3, 2).
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