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Quadratic graphs - Coggle Diagram

- - - - use the discriminant >/=/< 0 to check
        
        e.g.
        
        x^2 - 2x + 1
        
        discriminant = (-2)^2 - 4(1)(1)
        
        .= 4 - 4
        
        .= 0 (1 real root)
  - - - use the discriminant equation/inequality to find the value/values of k
        
        e.g.
        
        x^2 - 2x + k has 1 root
        
        (-2)^2 - 4(1)(k) = 0
        
        4 - 4k = 0
        
        4k = 4
        
        1 more item...
  - - - sub in the equations and make it a quadratic formula to use discriminant >/=/< 0 to check
        
        e.g.
        
        y = x^2 - 2x + 1 and line y = 2x + 1
        
        sub (1) into (2)
        
        2x + 1 = x^2 - 2x + 1
        
        x^2 - 4x = 0
        
        1 more item...
- - - - when discriminant
        
        is > 0
        
        2 real and distinct roots
        
        as the result of the square root will have ±√discriminant, so there will be two answers
        
        is = 0
        
        1 real root
        
        as ±√0 will result in ±0, which is just 0, so there will be one answer
        
        is < 0
        
        No real roots
        
        as there is no real answer to the square root of a negative number
      - this comes from the square root part of the formula
        
        (-b ± √(b^2 - 4ac)) / 2a