Please enable JavaScript.
Coggle requires JavaScript to display documents.
Math Sub bab 1.1-1.4 - Coggle Diagram
Math Sub bab 1.1-1.4
Quadratics
1.1 Solving Quadratic Equations by Factorisation
Equation is written in the form → ax² + bx + c = 0
Equation is solved by → factorising into (px + q)(rx + s) = 0
Roots are found by → zero-product rule
Example shows → (x + 2)(x – 3) = 0 → x = –2 or 3
1.2 Completing the Square
Quadratic is transformed into → (x + d)² + e = 0
Method is useful for → solving & graphing quadratics
Form gives → vertex form a(x – h)² + k
Example becomes → x² + 6x + 5 = (x + 3)² – 4
1.3 The Quadratic Formula
Any quadratic can be solved by → x = (–b ± √(b² – 4ac)) / 2a
Formula is derived from → completing the square
Nature of roots is determined by → discriminant Δ = b² – 4ac
If Δ > 0 → there are 2 real roots
If Δ = 0 → there is 1 repeated root
If Δ < 0 → there are no real roots
Formula works for → all quadratic equations
1.4 Solving Simultaneous Equations (Linear & Quadratic)
System consists of → one linear equation and one quadratic
Algebraic method is → substitute linear into quadratic
Step 1 → make x or y the subject in linear equation
Step 2 → substitute into quadratic
Step 3 → solve quadratic for variable
Step 4 → back-substitute to find the other variable
Graphical meaning is → intersection of line and parabola
2 intersections → 2 solutions
tangent → 1 solution
no intersection → no solution
Example shows → y = x² – 4 and y = 2x – 1 intersect at (–1, –3) and (3, 5)