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.
