1. A-REI.4 Solve quadratic equations in one variable.
Quadratic Formula
N-CN.7 Solve quadratic equations with real coefficients that have complex solutions.
A-REI.4 Solve quadratic equations in one variable.
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

2. Discriminant
Tells the type and number of solutions to a quadratic equation.

3. Discriminant Negative number: 2 complex solutions
Zero: 1 real solution
Positive number: 2 real solutions
Perfect square: rational
Non perfect square: irrational

4. Examples
EX: 5 𝑥 2 −𝑥−1=0 EX: 𝑥 2 +3𝑥=−6 EX: 2 𝑥 2 −𝑥−15=0 EX: 𝑥 2 =16𝑥−64

5. Quadratic Formula 𝒙= −𝒃± 𝒃 𝟐 −𝟒𝒂𝒄 𝟐𝒂
Use to solve quadratic equations that CANNOT be factored
Set = 0
Substitute values of a, b, and c into formula, then simplify.
𝒙= −𝒃± 𝒃 𝟐 −𝟒𝒂𝒄 𝟐𝒂

6. Examples
EX: 𝑥 2 −𝑥+1=0 EX: 3 𝑥 2 +8𝑥=3 EX: 𝑥 2 −6𝑥+3=0 EX: 2 𝑥 2 +4=7𝑥

7. Word Problems
An object is dropped from a height of 1700 feet above the ground. The function ℎ=−16 𝑡 gives the object’s height h in feet during free fall at t seconds. When will the object be 1000 feet above the ground?
The quadratic function ℎ=−0.01 𝑥 𝑥+2 models the height of a punted football. The horizontal distance in feet from the point of impact with the kicker’s foot is x and h is the height of the ball in feet. If the nearest defensive player is 5 feet from the point of impact, how high must the player reach to block the punt?

8. Solving Quadratics Review
Is it missing the middle term?
Solve by taking the square root
Can you factor?
GCF, Backwards FOIL, Difference of Squares, Bottoms Up
If you cannot use square root or factor:
Solve by completing the square (only if no a)
Solve using the quadratic formula

9. Examples EX: 𝑥 2 +49=0 EX: 𝑥 2 −2𝑥−17=0 EX: 𝑥 2 −𝑥=30 EX: 3𝑏 2 =10𝑏+32
Solve the quadratic equations by factoring, using square roots, completing the square, or using the quadratic formula.
EX: 𝑥 2 +49=0 EX: 𝑥 2 −2𝑥−17=0
EX: 𝑥 2 −𝑥=30 EX: 3𝑏 2 =10𝑏+32
EX: 2 𝑥 2 +2𝑥+3=0 EX: 3 𝑥 2 +36=0