1. The Quadratic Formula and the Discriminant.
Completing the Square.
The Quadratic Formula and the Discriminant.
What you’ll learn
To solve quadratic equations by completing
the square. To solve quadratic equations using
the quadratic formula. To find the number of
solutions of a quadratic equation.
Vocabulary
Completing the square. Quadratic formula.
Discriminant.

2. Take a note: A very important note:
In general, you can change the expression
into a perfect square trinomial by adding
This process is called completing the square.
The process is the same whether b is positive
or negative.
Example:

3. Problem 1: Solving
What are the solutions of the equation ?
Your turn
Answer
-13,19

4. Problem 2: Solving
What are the solutions of the equation ?
Your turn
Answer
-2.21,-6.79

5. Take a note: You can find the solution(s) of any
quadratic equation using the quadratic formula
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
Example:
𝑥= −3± −4(2)(−5) 2(2)
= −3±
= −3±7 4
𝑥= −3−7 4
= −10 4
𝑥= −3+7 4
= 4 4
𝑥=− 5 2
𝑥=1

6. Problem 3: Using the Quadratic Formula
What are the solutions of Use the QF
Make the equation =0
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
𝑥= −(−2)± (−2) 2 −4(1)(−8) 2(1)
= 4±

7. What are the solutions of .Use the QF
Your turn
What are the solutions of Use the QF
Answers:
a)-3,7
b) -2,5
Your turn again:
Which method would you choose to solve each equation?
Answers

8. Problem 4: Finding Approximate Solutions.
In the shot put, an athlete throws a heavy metal ball
through the air. The arc of the ball can
be model by the equation
where x is the horizontal distance,
in meters, from the athlete and y is
the height, in meters of the ball. How
far from the athlete will the ball land?
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
𝑥= −0.84± −4(−0.04)(2) 2(−0.04)

9. Your turn Answer: 144.8 ft A batter strikes a baseball. The equation
models its path, where x is the horizontal distance in ft., the ball
travels and y is the height, in feet,
of the ball. How far from the batter will the ball land?
Rounded to nearest tenth of a foot.
Answer:
144.8 ft

10. 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
Take a note: In this formula

11. Problem 5: Using the Discriminant
How many real solutions does
Because the discriminant is negative has no real solutions
Your turn
Answer: 2

12. Classwork odd Homework even
TB pgs exercises 7-30 and 34-42
pgs exercises 7-40