Algebra Know-It-ALL

values when the parabola opens upward. When a parabola opens downward, it has a single
point at which it “peaks.” This point is called the absolute maximum.
Sometimes the term extremum is used in reference to an absolute maximum or an abso-
lute minimum in the graph of a function. It means, as you might guess, “absolute extreme
value.” In a parabola, the extremum may also be called the vertex.

Alternative function notation

Sometimes a quadratic function is given a name such as f, and then its value is denoted
by that name with the independent variable in parentheses afterward. For example, we
might write

f (x)=x^2 + 2 x+ 1

instead of

y=x^2 + 2 x+ 1

x

y

x=r x=s

y= 0 y= 0

y> 0

Absolute maximum

xmax= (r+s)/ 2

Figure 24-3 Graph of a quadratic function with two

real zeros when the coefficient of x^2 is

negative. The parabola opens downward,

crosses the x axis twice, and has an absolute

maximum with y > 0.

Two Real Zeros 399