Algebra Know-It-ALL

The absolute minimum is at the point (r, 0). The parabola seems to “sit upon” the x axis.

Parabola opens downward

Figure 24-6 illustrates the graph of another generic quadratic function with one real zero. Let’s
call it r, as before. Also as before, the point (r, 0) on the parabola is tangent to the x axis. If
the quadratic function is

y=ax^2 +bx+c

thena < 0 because the parabola opens downward. The root of the equation

ax^2 +bx+c= 0

can again be found using the quadratic formula. And just as before, the discriminant in the
quadratic formula is equal to 0, so

r=−b/(2a)

x

y

x=r

y= 0

Absolute minimum

x=q

y=k

Liney=k

wherek> 0

x=p

y=k

Figure 24-5 Graph of a quadratic function with one

real zero when the coefficient of x^2 is

positive. The parabola opens upward, is

tangent to the x axis at a single point, and

has an absolute minimum with y= 0.

A line with the equation y=k, where

k > 0, intersects the parabola twice.

One Real Zero 403