module 11 topic 1
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Module 11 Topic 1 Graphing and Solving Quadratic
EquationsGoal 4: The learner will use relations and
functions to solve problems and justify results.Objective 4.02: Graph, factor, and evaluate
quadratic functions to solve problems.
Graphs of Quadratic Equations are called
Parabolas
Vertex
Axis of Symmetry
y = ax2 + bx + c
Click on the parabola
below to watch a short clip on graphing quadratics.
a is a coefficient that determines if the parabola opens upward or downward
a, b and c are used to find the vertex using the following formula
Example 1: Determine if the parabola for the following functions open upward or downward.
a) y = x2 + 4x - 6
The graph opens upward because the value of a is 1 which is positive.
b) y = -3x2 + 6x – 2
The graph opens downward because the value of a is -3 which is negative.
Example 2: Find the Vertex
Let’s identify a, b and c Use the vertex formula to find the vertex.
y = x2 – 6x + 4
a = 1
b = -6
c = 4
Example 3: Find the Vertex when b = 0
Let’s identify a, b and c Use the vertex formula to find the vertex.
y = -3x2 + 6
a = -3
b = 0
c = 6
Solving Quadratic Equations can be done by factoring or graphing.
Set each factor equal to zero and solve for
x.y = x2 + 5x + 6
a = 1 b = 5 c = 6We need to find two factors that
have a product of 6 and a sum of 5.
So 2 and 3 will work for this problem.
Click on the parabolas to watch a short clip about solving quadratics.
2g3 =62 + 3 =5
y = (x + 2)(x + 3)
x + 2 = 0
x + 2 – 2 = 0 – 2
x = -2
x + 3 = 0
x + 3 – 3 = 0 - 3
x = -3
The quadratic equation crosses the x-axis at -2
and -3. These are called the roots, zeros, or
solutions.
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