Download Quadratic Functions (second degree polynomial functions)

Graphing and Parts of a Parabola
Quadratic Functions
(second degree polynomial functions)
“functions that have an exponent of 2 for the highest power of x”
 Equation Format :
y = ax2 + bx + c
(a, b, c are coefficients AND x, y are variables).

Graph Shape: PARABOLA --U shaped graph

Quadratics are FUNCTIONS because each “x “ value in the domain yields (produces)
only ONE “y” in the range.
Parts of a Parabola
A) Minimum/Maximum (also called “TURNING POINT or “VERTEX)
The lowest/highest point (ordered pair x,y) on a parabola.
B) Axis of Symmetry
A line (with the equation in the form x=__)
where the parabola is separated into 2 symmetrical sections.
On the graphs we will be investigating the line is a vertical line.
The access of symmetry always cuts through the vertex.
C) Roots (also called x-intercepts or solutions).
Roots are found where the parabola crosses the x-axis.
A parabola can cross 2 times, 1 time, or 0 times.
The x value on this point is called the root.
In this case (as opposed to a linear), the y coordinate is always 0.
Minimum: (3, -4)
(point)
Maximum: (-4, 5)
(point)
Axis of Symmetry:
x = 3 (line)
Axis of Symmetry:
x = -4 (line)
Roots: {1, 5}
(x-values at
x-intercept points.)
Roots: {-1, -7}
(x-values at
x-intercept points.)