The document discusses quadratic equations and their functions, focusing on roots, their nature, and maximum or minimum values. It elaborates on the conditions determining the number of roots based on the discriminant and how the graph behaves relative to the x-axis. Additionally, it covers the concept of quadratic inequalities and the manipulation of expressions to find new roots.

1. QUADRATIC EQUATIONS AND
FUNCTIONS
1. Roots of Quadratic Equations
2. The Nature of the Roots
3. Maximum or Minimum Values
4. Quadratic Inequalities

2. Roots of Quadratic Equations

3. Factorize “2”
Express as a single fraction
Manipulation of
Express as a single fraction

4. New Quadratic Equations:
Sum of the Product of the
New Roots New Roots
Previous Quadratic Equations:

5. Sum of the
New Roots
Product of the
New Roots
Sum of the
New Roots
Product of the
New Roots

6. The Nature of the Roots
The nature of the roots is determined by the values of DISCRIMINANT (D)
The equation has TWO The graph cuts the x-axis
REAL & DISTINCT ROOTS at TWO points
The equation has EQUAL The graph touches the x-
OR COINCIDENT ROOTS axis at ONE points
The equation has NO The graph DOESN’T touch
ROOTS the x-axis
The equation has REAL
The graph cuts the x-axis
ROOTS

7. Rearrange the equation, RHS
must be “0”
The equation has equal roots
The graphs intersects with x-axis at one point
Rearrange the equation, RHS
must be “0”
No real roots
The graphs doesn’t intersect with x-axis