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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Solving Equations Using the Quadratic Formula

  • You can use the Quadratic Formula to solve any quadratic equation.
  • If you do not see an easy way to factor a quadratic equation, use the formula.
  • The discriminant is the radicand in the Quadratic Formula. Use it to determine the number of real roots of a particular quadratic equation.
  • If the discriminant is positive, the equation has 2 real roots.
  • If the discriminant is 0, it has one rational root.
  • If the discriminant is negative, it has no real roots.

Solving Equations Using the Quadratic Formula

Solve using the quadratic formula:
5j2 + 6j + 1 = 0
  • j = [( − 6 ±√{62 − 4( 5 )( 1 )} )/2(5)]
  • j = [( − 6 ±√{16} )/10]
j = − [1/5], − 1
Solve using the quadratic formula:
8a2 − 11a + 3 = 0
  • a = [( − ( 11 ) ±√{( 11 )2 − 4( 8 )( 3 )} )/2( 8 )]
  • a = [( − ( 11 ) ±√{25} )/16]
  • a = [(11 ±5)/16]
a = 1,[3/8]
Solve using the quadratic formula:
b2 + 12b − 30 = 0
  • b = [( − 12 ±√{122 − 4( 1 )( 30 )} )/2(1)]
b = [( − 12 ±√{24} )/2]
Solve using the quadratic formula:
9r2 = 14r − 3
  • 9r2 − 14r + 3 = 0
  • r = [( − ( − 14 ) ±√{( − 14 )2 − 4( 9 )( 3 )} )/2( 9 )]
r = [(14 ±√{88} )/18]
Solve using the quadratic formula:
4s2 = − 7s − 2
  • 4s2 + 7s + 2 = 0
  • s = [( − 7 ±√{72 − 4( 4 )( 2 )} )/2( 4 )]
s = [( − 7 ±√{17} )/8]
Solve using the quadratic formula:
20m2 = 25m − 5
  • 4m2 = 5m − 1
  • 4m2 − 5m + 1 = 0
  • m = [( − ( − 1 ) ±√{( − 5 )2} − 4( 4 )( 1 ))/2(4)]
  • m = [(1 ±√9 )/8]
  • m = [(1 ±3)/8]
m = [1/2],[1/4]
Solve using the quadratic formula:
14y2 = 49y + 21
  • 2y2 = 7y + 3
  • 2y2 − 7y − 3 = 0
  • y = [( − ( − 7 ) ±√{( − 7 )2 − 4( 2 )( − 3 )} )/2( 2 )]
y = [(7 ±√{73} )/4]
Solve using the quadratic formula:
54n2 = − 81n + 18
  • 6n2 = 9n + 2
  • 6n + 9n − 2 = 0
  • n = [( − 9 ±√{92 − 4( 6 )( − 2 )} )/2( 6 )]
n = [( − 9 ±√{129} )/12]
Determine the number of real roots of 11x2 + 6x + 7 = 0D = 62 − 4( 11 )( 7 )
  • D = 36 − 308
  • D = − 272
No real solutions
b2 + 12b − 30 = 0
  • b = [( − 12 ±√{122 − 4( 1 )( 30 )} )/2( 1 )]
b = [( − 12 ±√{24} )/2]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Solving Equations Using the Quadratic Formula

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Quadratic Formula 0:17
    • Standard Form
    • Example
  • Discriminant 3:14
    • Two Solutions and Both Real
    • One Real Solution
    • No Real Solutions
  • Example 1: Solve the Equation 6:25
  • Example 2: Solve the Equation 8:42
  • Example 3: Solve the Equation 12:02
  • Example 4: Number of Real Roots 15:23