Vocabulary
Square Roots
Simplifying Radicals
Graphing Quadratics
Quadratic Formula
& Discriminants
100
What is a perfect square?
    A perfect square is the square of an integer.
      √4=2 ∴ 4 is a perfect square
        √49=7 ∴ 49 is a perfect square
100
What is √100?
10
100
What is √40?
    √40
      =√(4 x 10)
        =2√10
100
How do you find the x-coordinate of the vertex of a parabola?
-b/(2a)
100
What is the quadratic formula?
(-b±√(b^2-4ac))/2a
200
What is the standard form of the quadratic equation?
ax^2+bx+c=0,where a≠0
200
What is √122?
11.0454
200
What is √54?
√54
    = √(9 x 6)
      = 3√6
200
How do you know if a parabola opens up or down?
    if a is positive, the parabola opens up
      if a is negative, the parabola opens down
200
Solve using the quadratic formula: x^2 + 9x = -14
    x^2 + 9x + 14 = 0 were a=1, b=9, and c=14
      (-9±√(9^2-4(1)(14)))/(2(1))
        (-9±√(81-56))/2
          (-9±√25)/2
            (-9±5)/2
              (-4)/2= -2 and (-14)/2= -7
300
What is the highest or lowest point of the parabola called?
The vertex.
300
Which of the following is not a perfect square: 64, 144, 289, 702, 900, 1024, 1332?
702 & 1332
300
What is 3 x (√(16/4))?
    =3(4/2)
      =3(2)
        =6
300
Sketch the graph of the function: y = x^2 - 2x - 3
    Vertex (1 , -4)
      X: -2 -1 0 1 2
        Y: 5 0 -3 -4 -3
300
Find the x-intercepts of the graph using the quadratic formula.
    y = x^2 + 4x - 5
    y = x^2 + 4x - 5 were a=1, b=4, and c=-5
      (-4±√(4^2-4(1)(-5)))/(2(1))
        (-4±√(16+20))/2
          (-4±√36)/2
            (-4±6)/2
              (2)/2= 1 and (10)/2= 5
400
What are the points that intersect the x-axis called?
Roots of a Quadratic Equation.
400
What is √(-25)?
This is not a real number, it is imaginary.
400
What is 1/√(10)?
    =[1/√(10)] * [√(10)/√(10)]
      =√(10)/1/√(100)
        =√(10)/10
400
What are some ways quadratics are used in real life?
    • Finding Profit
      • Finding the stopping distance of a car traveling at a specific speed.
        • Creating the lens of your glasses
          • Throwing a Ball
            • Shooting an Arrow
              • Firing a Missle
400
Find the value of the discriminant to determine whether x^2 - 3x -4 = 0 has two, one, or no solutions.
    Identify a = 1, b = -3, and c = -4
      Substitue values for a, b, c
        b^2 - 4(a)(c) = (-3)^2 - 4(1)(-4)
          = 9 + 16
            = 25 Since the discriminant is positive, the equation has two solutions.
500
What is the discriminant and what can it be used to find?
    The discriminant is the expression inside the radical and can
      be used to find the number of solutions of the
        quadratic equation.
          √(b^2-4ac)
500
What is √(75×3)?
√(225) = 15
500
What is √(14/21)?
    =√(14/21)
      =√(294)/21
        =7√(6)/21
          =√(6)/3
500
Find the roots of the quadratic by factoring the polynomial: y = x^2 - 11x + 24
    Factors of 24 that add to 11 are (8)(3) = 24
      (x - 8)(x - 3)= 0
        x = 8, 3
          Check: x^2 -3x -8x + 24
            x^2 -11x + 24
500
Find the value of the discriminant to determine whether x^2 - 4x + 4 = 0 has two, one, or no solutions.
    Identify a = 1, b = -4, and c = 4
      Substitue values for a, b, c
        b^2 - 4(a)(c) = (-4)^2 - 4(1)(4)
          = 16 - 16
            = 0 The discriminant is 0, so the equation has one solution.
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