Quadratics

• What happens if b2-4ac> 0 or b2-4ac<0

  • >0 when x<smaller number & x> bigger number
  • <0 when smaller number<x<bigger number
• What defines a quadratic function or equation?

  • A function or equation in which the highest power of x is 2
• How to do higher complete the square?

  • e.g. 2x2+4x-8
  • 2(x2+2x)-8
  • 2(x+1)2-1)-8
  • 2(x+1)2-2-8. 29
• What is the expanded form of a quadratic function?

  y = ax² + bx + c
• What is the factorized form of a quadratic function?

  y = a(x - m)(x - n)
• What does the Completed Square Form reveal about the quadratic function?

  The turning point is (h, k)
• What information does the factorized form provide?

  The roots, x = m and x = n
• What are the National 5 Skills covered in this section?

  • Finding the equation of a quadratic function from a turning point
  • Solving quadratics
  • Sketching quadratics
  • Determining the nature of the roots using the discriminant
• What skills are required to find the equation of a quadratic function from a turning point?

  • Use completed square form: y = k(x - m)² + q
  • Substitute the turning point to find the values of k, m, and q
  • Use root form: y = k(x - m)(x - n)
  • Substitute the roots to find k and then the turning point
• What are the three methods to find the value of k in a quadratic function?

  • Graphically
  • Algebraically
  • Using the Quadratic Formula
• What are the two higher-level skills for solving quadratic equations?

  • Solving quadratics by rearranging
  • Completing the square for non-unitary coefficients
• What formula is used to determine the nature of the roots of a quadratic equation?

  $D =$$b² - 4ac$
• Which form of quadratic equation uses $y =$$k(x + p)² +$$q?$


  Completed square form
• Which form of quadratic equation uses $y =$$k(x - m)(x - n)?$


  Root form
• How is the discriminant used in quadratic equations?

  • To determine the nature of the roots
  • To find the points of intersection between a quadratic curve and the x-axis
• What are the three results that matter when calculating the discriminant?

  • If $D > 0,$ there are two distinct real roots
  • If $D =$$0,$ there are two equal real roots
  • If $D < 0,$ there are no real roots
• When is it necessary to rearrange a quadratic equation before solving it?

  If the quadratic equation is not equal to zero
• What higher-level skills are covered under National 5 Skills?

  • Solving quadratics by rearranging
  • Completing the square for non-unitary coefficients
• What technique is used to solve quadratic equations in the form $ax² +$$bx +$$c =$$0$ where $a ≠ 1?$


  Completing the square with a non-unitary coefficient of x
• What are the steps to solve a quadratic inequation?

  1. Find the roots.
  2. Draw a sketch.
  3. Answer the question by determining the range of x where the inequation is true
• How do you determine the values of k for which $3x² +$$kx +$$3 =$$0$ has equal roots?


  The discriminant must be zero: $b² - 4ac =$$k² - 4(3)(3) =$$0,$ which leads to $k =$$± \sqrt{36} =$$±6$