This document provides instructions for solving quadratic equations by completing the square. It explains that you can complete the square by adding a constant to both sides of the equation to make the quadratic term a perfect square. You then take the square root of both sides to solve for x. It also notes that when the leading coefficient is not 1, you must first divide both sides by the coefficient a. Finally, it shows that completing the square allows you to derive the quadratic formula, which can be used to solve any quadratic equation in standard form.

1. Solving for Roots By
Completing the square
• You can complete the square by adding a constant to both
sides of the equation
• Add the constant that will turn the quadratic into a perfect
square
• Take the square root of both sides
• Solve for x
Ex. Solve x2 ­ 4x + 2 = 0
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2. When the leading coefficient is not equal to one
• Divide both sides of the equation by the
coefficient a before completing the square
Ex. Solve by completing the square 2x2 ­ 6x ­7 = 0
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3. General Solution to Quadratics by
Completing the Square
(building the quadratic formula)
Solve for x by completing the square
ax2 + bx +c = 0
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4. The completing square allows us to find that we can find the
solutions using the
Quadratic Formula
You can use the quadratic formula to solve any quadratic equation.
To use the equation you first need to set up the equation in
standard form
ax2 + bx + c = 0
Then you can substitute a, b, and c into the formula
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6. Ex. Sove x2 + 3x ­ 9 = 0
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7. If you remember from our quadratics unit, we can
find the x value at the vertex, and the axis of
symmetry by
h =
The quadratic formula can be represented by two
fractions.
The first part is the h value.
The second part is the horizontal distance from the
axis of symmetry to the x intercepts in both the
positive
and negative direction.
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