Quadratic Equations & Quadratic Functions

Quadratic Equations & Quadratic Functions Last Minute Revision Myhometuition.com

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Quadratic Equations and Quadratic Functions Quadratic Inequalities IMPORTANT! Make sure you know this.

General Form f ( x)  ax 2  bx  c

where a, b, and c are constants and a  0. *Note that the highest power of an unknown of a quadratic function is 2.

a  0  minimum   (smiling face) a  0  maximum   (sad face)

Completing the Square

Example 1

f ( x)  a ( x  p ) 2  q

(i) (ii) (iii) (iv)

the value of x, x   p min./max. value = q min./max. point = ( p, q) equation of axis of symmetry, x   p

Completing Square to find Maximum/Minimum STEP 1: Make sure that a = 1, if not factorise 1  1  STEP 2: Put in  b 2    b 2  2  2  STEP 3: Completing the square

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Example 2

Nature of Roots (Combination of Straight Line and Curve) When you solve the equations of a line and a curve simultaneously and form quadratic equation, ax 2 + bx + c = 0, the discriminant, b2 – 4ac, gives information about the number of points of intersection.

If b2 – 4ac > 0 the line and curve intersect in 2 distinct points.

If b2 – 4ac = 0 the line is the tangent to the curve..

If b2 – 4ac < 0 the line and curve not intersect.

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