quadratic equations
DESCRIPTION
This presentation includes the roots of quadratic equation, the nature of the roots, minimum and maximum values and quadratic inequalityTRANSCRIPT
QUADRATIC EQUATIONS AND FUNCTIONS
1. Roots of Quadratic Equations2. The Nature of the Roots3. Maximum or Minimum Values4. Quadratic Inequalities
Roots of Quadratic Equations
Factorize “2”
Express as a single fraction
Manipulation of
Express as a single fraction
New Quadratic Equations:Sum of the New Roots
Product of the New Roots
Previous Quadratic Equations:
Sum of the New Roots
Product of the New Roots
Sum of the New Roots
Product of the New Roots
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
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”