factorised form of quadratics

• What does the term "roots" refer to in quadratics?

  Points where the graph crosses the x-axis
• What is the quadratic equation given in the study material?

  y = 2x² + 7x - 15
• When do the roots occur in the quadratic equation?

  When y = 0
• What is the factored form of the quadratic equation?

  y = (2x - 3)(x + 5)
• What equation is set to zero to find the roots?

  0 = (2x - 3)(x + 5)
• What does the equation a x b = 0 imply?

  Either a = 0 or b = 0
• What is the value of x when 2x - 3 = 0?

  x = $\frac{3}{2}$
• What is the value of x when x + 5 = 0?

  x = -5
• What is the turning point (T.P.) of the quadratic y = (x - 4)(x - 10)?

  T.P. = (7, -9)
• How do you calculate y when x = 7 for the equation y = (x - 4)(x - 10)?

  y = (3)(-3) = -9
• What is the axis of symmetry for the quadratic y = (x - 4)(x - 10)?

  x = 7
• How do you find the y-intercept of a quadratic equation?

  Set x = 0 in the equation
• What is the y-intercept for the equation y = (x - 4)(x - 10)?

  y = 40
• What is the inequality given in the study material?

  19 + x > 15 + 3(x - 2)
• What is the simplified form of the inequality 19 + x > 15 + 3(x - 2)?

  5 > x
• What is the expression to be converted to the form (x - a)² + b?

  x² - 60x + 8
• What is the completed square form of x² - 60x + 8?

  (x - 30)² - 892
• What are the coordinates of the turning point of the graph of y = x² - 6x + 8?

  (3, 4)
• How do you calculate y when x = 0 for the equation y = (x - 3)² - 1?

  y = 8
• What is the axis of symmetry for the equation y = (x + 7)² - 4?

  x = -7
• What are the coordinates of the turning point for the equation y = (2x + 3)² + 12?

  (-3, 12)
• What is the expression for the turning point of the graph of y = (x - 4)² - 17?

  (4, -17)
• What is the axis of symmetry for the equation y = (x - 4)² - 17?

  x = 4
• What is the value of x when solving the equation 36x = 200?

  x = $\frac{200}{36}$
• What is the solution to the equation 12x - 15 = 36x?

  x = -\frac{15}{24}
• What is the value of x when -\frac{5}{8} = x?


  x = -\frac{5}{8}
• What are the steps to factor a quadratic equation?

  1. Set the equation to zero.
  2. Factor the quadratic expression.
  3. Solve for x using the zero product property.
• What are the characteristics of the turning point of a quadratic graph?

  • The vertex of the parabola
  • Indicates maximum or minimum value
  • Axis of symmetry passes through it
• What are the methods to find the y-intercept of a quadratic function?

  • Substitute x = 0 into the equation
  • Calculate the resulting y value
• What are the forms of quadratic equations?

  1. Standard form: y = ax² + bx + c
  2. Factored form: y = a(x - r1)(x - r2)
  3. Vertex form: y = a(x - h)² + k