1. 10
Quadratic Equations

2. 10.1 Solving Quadratic Equations by the Square Root Property
Objectives
1. Review the zero-factor property. 2. Solve equations of the form x2 = k, where k > Solve equations of the form (ax + b)2 = k, where k > Use formulas involving squared variables.

3. Solve Equations of the Form x2 = k, Where k > 0
Square Root Property
If k is a positive number and if x2 = k, then

4. Solve Equations of the Form x2 = k, Where k > 0
Example 2
Solve each equation. Write radicals in simplified form.
By the square root property or

5. Solve Equations of the Form (ax + b)2 = k, Where k > 0
Example 3
Solve each equation.
Square root property
Subtract 5.

6. Solve Equations of the Form (ax + b)2 = k, Where k > 0
Example 3 (concluded)
Solve each equation.
Square root property
Add 4.

7. Solve Equations of the Form (ax + b)2 = k, Where k > 0
Example 4 Solve the equation.
CAUTION
These solutions in Example 4 are fractions that cannot be simplified. Note that 4 is not a common factor in the numerator.

8. Solve Equations of the Form (ax + b)2 = k, Where k > 0
Example 5
Solve the equation.
Because the square root of –25 is not a real number, there
is no real number solution for this equation. The solution
set is

9. Use Formulas Involving Squared Variables
Example 6
To propose, John took Amy on a hot air balloon ride. To celebrate their engagement, he brought champagne. However, when he rose his arm to toast, he knocked the bottle of champagne from their basket. The formula s = ½at2 + s0 gives the height of the bottle of champagne above the ground, given its acceleration, a, its initial height above the ground, s0, and time, t, in seconds. How long will it take the bottle of champagne to hit the ground if John and Amy’s basket was 1610 ft high, and the bottle fell with an acceleration of 32.2 ft/sec2? (Hint: a = –32.2, since the bottle of champagne was falling.)

10. Use Formulas Involving Squared Variables
Example 6 (concluded)
We will solve the equation s = ½at2 + s0 for t, letting a = –32.2 and s0 = When the bottle hits the ground, its height, s, will be 0. So, we have the equation
Since a time of –10 seconds has no meaning, the solution is that it took the bottle 10 seconds to hit the ground.