Download - Quadratic Equations

Transcript
Page 1: Quadratic Equations

QUADRATIC EQUATIONS AND FUNCTIONS

1. Roots of Quadratic Equations2. The Nature of the Roots3. Maximum or Minimum Values4. Quadratic Inequalities

Page 2: Quadratic Equations

Roots of Quadratic Equations

Page 3: Quadratic Equations

Factorize “2”

Express as a single fraction

Manipulation of

Express as a single fraction

Page 4: Quadratic Equations

New Quadratic Equations:Sum of the New Roots

Product of the New Roots

Previous Quadratic Equations:

Page 5: Quadratic Equations

Sum of the New Roots

Product of the New Roots

Sum of the New Roots

Product of the New Roots

Page 6: Quadratic Equations

The Nature of the RootsThe nature of the roots is determined by the values of DISCRIMINANT (D)

The equation has TWO REAL & DISTINCT ROOTS

The equation has EQUAL OR COINCIDENT ROOTS

The equation has NO ROOTS

The equation has REAL ROOTS

The graph cuts the x-axis at TWO points

The graph touches the x-axis at ONE points

The graph DOESN’T touch the x-axis

The graph cuts the x-axis

Page 7: Quadratic Equations

The equation has equal rootsThe graphs intersects with x-axis at one point

No real rootsThe graphs doesn’t intersect with x-axis

Rearrange the equation, RHS must be “0”

Rearrange the equation, RHS must be “0”


Top Related