A quadratic function has a U-shaped graph called a
parabola. A quadratic function can be written in the
form ax2 + c, where a is called the leading coefficient.
If a is positive, the parabola opens up.
If a is negative, the parabola opens down. If the
absolute value of a is greater than 1, then the
parabola will be narrower than y = x2. If the
absolute value of a is less than 1, then the parabola
will be wider than y = x2.
The vertex of a parabola is the point from which the
graph opens up or down.
Adding values to and subtracting values from ax2
translates the vertex along the y-axis.
In the form y = (x - a)(x - b), the vertex is
located at (a, b) .
The vertex is at (0, 4). Because the leading
coefficient is positive, the graph opens up. Because
the leading coefficient is less than 1, the graph will
be wider than y = x2.