Introduction to Quadratic
Functions
Section 5.1
 Quadratic function – any function that can be
written in the form
f  x   ax 2  bx  c, where a  0
 Ex. 1 Let g(x) = (4x + 3)(x – 6). Show that g
represents a quadratic function. Identify a, b,
and c when the function is written in the form
g  x   ax 2  bx  c
Ex.1 continued
 g(x) = (4x + 3)(x – 6)
FOIL to simplify
2
4x
 24x  3x  18
 g(x) =
2
 g(x) = 4x  21x  18
 a = 4, b = -21, c = -18
Ex.2
 g(x) = (2x - 5)(x – 2)
2
2x
 4x  5x  10
 g(x) =
 g(x) = 2x 2  9x  10
 a = 2, b = -9, c = 10
Graphing quadratic functions
 Graphs as a parabola.
 If a > 0, the
 parabola
 opens up.
 If a < 0, the
 parabola
 opens down.
 If the parabola opens up, the vertex is the
lowest point. The y-coordinate of the vertex
is the minimum value of f(x).
 If the parabola opens down, the vertex is the
highest point. The y-coordinate of the vertex
is the maximum value of f(x).
 State whether the parabola opens up or down
and whether the y-coordinate of the vertex is
a minimum value or maximum value of the
function.
 Ex. 3
 f(x) = 5x 2  3x
 a = 5 so the parabola opens up and the y
coordinate of the vertex in the minimum value
of the function
 Ex 4
 h(x) = (5 – x)(2 + 3x)
 FOIL to see what a is.
 h(x) = 3x 2  13x  10
 a = -3 so the parabola opens down and the y-
coordinate of the vertex is the maximum
value