4.5 Quadratic Equations
Solving Quadratic Equations using inverse operations
When a quadratic equation is in the form of 𝑎𝑥 2 + 𝑐 = 0, you can solve it using
inverse operations.
1. Isolate the x2 term on one side of the equation.
2. Take the square root of each side of the equation. (do not forget the + when
taking the square root of a number.
Note:
When solving x2 = c using square roots:
 If c > 0, then 𝑥 2 = 𝑐 has two solutions: = ±√𝑐 .
 If c = 0, then 𝑥 2 = 𝑐 has one solution: x = 0.
 If c < 0, then 𝑥 2 = 𝑐 has no real solution.
Solving Quadratic Equations by Factoring
1. Rewrite the equation in standard form (𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0)
2. Set the expression in standard form equal to zero.
3. Factor the quadratic completely.
4. Set each factor equal to zero. (Zero-Product Property)
5. Solve each equation to get the possible solutions.
Recall:
Zero Product Property
If ab = 0, then a = 0 or b = 0
Algebra 2: Lesson 4-5 Quadratic Equations
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Example 1: Solve each quadratic equation using square roots.
a. x2 = 4
b. x2 = 5
c. x2 – 9 = 0
d. x2 – 16 = 0
e. x2 – 7 = 0
f. x2 – 15 = 0
Example 2: Solve each quadratic equation using square roots.
a. 3x2 – 48 = 0
b. 2x2 – 72 = 0
c. 3x2 – 27 = 0
Algebra 2: Lesson 4-5 Quadratic Equations
d. 4x2 – 16 = 0
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e. 2x2 – 18 = 0
f. 5x2 – 75 = 0
g. 3x2 – 18 = 0
h. 5x2 – 15 = 0
Example 3: Solve each quadratic equation by factoring.
a. 2x2 +10x = 0
b. 3x2 – 9x = 0
c. x2 + 9x = 0
d. 4x2 = 12x
Algebra 2: Lesson 4-5 Quadratic Equations
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e. 6x2 = 15x
f. 5x2 + 20x = 0
Example 4: Solve each quadratic equation by factoring.
a. x2 – 6x = 16
b. x2 – 10x + 16 = 0
c. x2 + 2x = 63
d. x2 + 9x = 22
e. x2 – 24x + 144 = 0
f. x2 – 7x = -12
Algebra 2: Lesson 4-5 Quadratic Equations
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Example 5: Solve each quadratic equation by factoring.
a. 5n2 – 15n – 20 = 0
b. 4x2 – x = 5
c. 7x2 + 18x = -8
d. 2x2 + 32 = -20x
e. 2x2 = 7x + 4
f. 2x2 = -5x + 12
Algebra 2: Lesson 4-5 Quadratic Equations
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Example 6: A basketball player shoots at a basket that is 10 feet from the floor.
The function d = -16t2 + 20t + 6, gives the distance from the ball to the floor in
feet. d: height the ball is above the floor in feet; t: time in seconds
a. Explain how the equation 10 = -16t2 + 20t + 6 can help you find when the ball is
at basket level.
b. Solve 10 = -16t2 + 20t + 6 by factoring. Which solution represents the time that
the ball passes through the basket.
c. Explain how the equation 0 = -16t2 + 20t + 6 can help you find when the ball hits
the ground.
d. Solve 0 = -16t2 + 20t + 6 by factoring. Which solution makes sense as the time
the ball hits the ground?
Homework: Solving Quadratic Equations HW Worksheet 1 (day 1)
p. 245 => 1 – 3; 6 – 12 (day 2)
Solving Quadratic Equations HW Worksheet (day 3)
Algebra 2: Lesson 4-5 Quadratic Equations
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