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