Ib Maths Hl Quadratic Equations Notes 42325y

QUADRATIC EQUATIONS A quadratic equation is a PLOYNOMIAL where the highest exponent is 2 (so the variable is raised to the 2nd power). How can you express a quadratic function? 4 GENRAL FORM: y = Ax2 + Bx + C VERTEX FORM: y = a(x-h)2 + k

y

3

2 from general form to vertex form you must to go ‘COMPLETE THE SQUARE’ 1

ROOT FORM: y = a(x-α)(x-β) −6

−4

−2

where α and β are the solutions to the quadratic x Equation a(x-α)(x-β) = 0 and (x-α) and (x-β) are 2 4 6 2 the factors of the equation ax – a(β + α)x + aαβ −1

example: y = (x – 2)(x – 3) −2 y = x2 -3x – 2x + 6 y = x2- 5x + 6 −3

−4

SOLVING QUADRATIC EQUATIONS: The solution of Ax2 + Bx + C = 0 identifies the x intercepts (roots, zeros) of the quadratic equation y = Ax2 + Bx + C . 1) 2) 3) 4)

Factoring Graphing Completing the square Quadratic formula