Algebra Know-It-ALL

Parabola opens upward

Figure 24-2 shows a generic graph of a quadratic function of x with two real zeros, which
we call r and s. At the points on the x axis where x=r and x=s, the parabola crosses. This
parabola opens upward. Imagine that its quadratic function is

y=ax^2 +bx+c

Thex-intercepts are r and s. They represent the roots of the equation

ax^2 +bx+c= 0

so they can be found using the quadratic formula. If r is the smaller of the two zeros and s is
the larger, then

r= [−b− (b^2 − 4 ac)1/2] / (2a)

and

s= [−b+ (b^2 − 4 ac)1/2] / (2a)

x

y

Figure 24-1 The graphs of quadratic functions with

real coefficients and a real constant are

always parabolas, and they always pass

the “vertical-line test” for a function.

Two Real Zeros 397