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Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
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Coordinate System
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The Slope of a Line
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What the Factored Form of a Quadratic can tell you about the graph
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Finding the GCF of a Set of Monomials
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Solving Equations with Radicals and Exponents
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Adding and Subtracting Rational Expressions
Laws of Exponents and Dividing Monomials
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Solving Quadratic Equations by Completing the Square
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Factoring Trinomials
Writing Decimals as Fractions
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Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
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Introduction to Fractions
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Solving Nonlinear Equations

In the following example, we find the solutions to a quadratic function by graphing the function and then finding the x-intercepts.


Given the function: f(x) = x2 + 8x +12

a. Graph the function.

b. Use the graph to find the solutions to x2 + 8x +12 = 0.


a. The graph of the function f(x) = x2 + 8x +12 is a parabola since it has the form y = ax2 + bx + c. Here, a = 1, b = 8, and c = 12.

To graph the parabola, first find the x-coordinate of the vertex and then calculate ordered pairs on either side of the vertex.

Here is the formula for the x-coordinate of the vertex. x
Substitute a = 1 and b = 8. x
Simplify.   = -4

Now, make a table of values by choosing values of x on either side of the x-coordinate of the vertex, x = -4.


x y














Finally, use the table to graph y = x2 + 8x +12.


The line x = -4 is the axis of symmetry of the parabola.

That is, if you fold the graph along the line x = -4 one side of the graph will lie on top of the other.


b. The graph crosses the x-axis at (-6, 0) and (-2, 0).

So, the solutions of x2 + 8x +12 = 0 are x = -6 and x = -2.

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