Chapter 3: Form 4_Quadratic Functions

CHAPTER 3: QUADRATIC FUNCTIONS

*A quadratic function has a variable with the highest power of 2 which is f(x) = ax² + bx + c = 0.

SHAPE OF THE GRAPH OF A QUADRATIC FUNCTION

*Generally, the shape of the graph of a quadratic function f(x) = ax² + bx + c = 0 has two shape whether ‘n’ shape or ‘u’ shape.

(a) ‘n’ shape when a > 0

(b) ‘u’ shape when a < 0

RELATIONSHIP BETWEEN THE POSITION OF THE GRAPH OF A QUADRATIC FUNCTION WITH THE TYPES OF ROOTS OF A QUADRATIC EQUATION

*The type of roots of a quadratic equation ax² +bx + c = 0 is determine by the value of b² – 4ac.

CASE 1:

*The graph f(x) intersects the x-axis at two different points.

*The equation f(x) = 0 has two different real roots.

  

CASE 2:

*The graph f(x) touches the x-axis at only one point.

*The equation f(x) = 0 has two equal reals roots.

CASE 3:

*The graph f(x) does not intersect the x-axis.

*The equation f(x) = 0 does not have any real roots.