February 14, 2016
Strategies for Factoring
1. Factor out any GCFs.
2. Factor a four term polynomial by pairs.
3. To factor
that add up to b.
find factors of c
4. See if you have a perfect square trinomial.
5. Look for a difference of squares.
6. Factor
Find factors of ac that add up to b.
Split the middle term into an equal sum
using those numbers.
7. Factor Sums and Differences of cubes
using the special rules.
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February 14, 2016
Solving Quadratic Equations by Factoring
The Zero-Factor Theorem
If a and b are real numbers and a • b = 0,
then a = 0 or b = 0.
To solve a quadratic equation using factoring,
1. Write the equation in standard form.
What is this?
2. Write the variable expression in factored form.
3. Use the zero-factor theorem to solve.
Solving Word Problems Using Quadratic Equations
1. Read the entire problem carefully.
2. Choose variable expressions to represent any
unknown values.
3. Write an equation based on the information in
the problem.
4. Solve the equation using an appropriate method.
5. Check to see if your solution is reasonable.
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February 14, 2016
Graphs of Quadratic Equations and Functions
An equation that can be written in the form
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y = ax + bx + c, where a, b, and c are real
numbers is a Quadratic Equation.
The line that divides the graph of a quadratic
function into two symmetrical halves is called
the Axis of Symmetry.
The equation for the axis of symmetry is
The lowest point on a parabola that opens up or
the highest point on a parabola that opens down
is called the Vertex. What are the coordinates
of the vertex on the graph above?
To find the coordinates of the vertex we will use
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February 14, 2016
A relation is a set of ordered pairs.
The domain is the set of all input values for a
relation. These are the x-values on a graph.
The range is the set of all output values for a
relation. These are the y-values on a graph.
A function is a rule that establishes a relationship
between an input and an output. For each input there
is exactly one output. We use the vertical line test to
determine if the graph of a relation is a function.
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