1. Solving Quadratic Equations Using Square Roots & Completing the Square

2. Using Square Roots to Solve a Quadratic Equation
When a quadratic equation is in the form
, it can be solved by isolating the
Quadratic term and using square roots.
Stress the fact that by definition, the square root of x2 = the absolute value of x. You may also need to remind students that the absolute value of x, is the distance away from zero. Point out that this method of isolating the quadratic and taking the square root of both sides is only possible because there is no linear term.

3. Solve Using Square Roots
Other Method:

4. Solve Using Square Roots
Stress to students that answers should be left exact unless otherwise stated.

5. Solve Using Square Roots
Stress to students that answers should be left exact unless otherwise stated.

6. Solve Using Square Roots
The square root
of a negative number
is undefined in the set
of real numbers.
What would happen if you graph this quadratic: The parabola would not have any x intercepts.

7. Solve Using Square Roots
Since this quadratic has only one solution, the vertex of the related parabola is on the x axis, therefore only one x intercept.

8. Solve Using Square Roots

9. Solve Using Square Roots
Perfect Square Trinomial
Binomial Square
Can we
solve this
quadratic
using a
different
method?
Students will need to recall that a perfect square trinomial factors into a binomial square. This example will help lead into completing the square.

10. Solve by Factoring

11. We will Use a method called Completing the Square to solve.
Solve by Factoring
We will Use a method called
Completing the Square to solve.

12. Solve by Completing the Square
NOT a Perfect
Square Trinomial
Move the constant
to the other side.
2. Add the square of
half the linear
coefficient to
both sides.
Factor the perfect
square trinomial
into a binomial
square.

14. Solve by Completing the Square
NOT a Perfect
Square Trinomial
Move the constant
to the other side.
2. Add the square of
half the linear
coefficient to
both sides.
Factor the perfect
square trinomial
into a binomial
square.

16. Solve by Completing the Square
NOT a Perfect
Square Trinomial
Move the constant
to the other side.
2. Add the square of
half the linear
coefficient to
both sides.
Factor the perfect
square trinomial
into a binomial
square.

18. Solve by Completing the Square
Divide both sides by
leading coefficient.
Move the constant
to the other side.
2. Add the square of
half the linear
coefficient to
both sides.
Factor the perfect
square trinomial
into a binomial
square.