Respuesta :
[tex]\bf \stackrel{f(x)}{0}=-(x+9)(x-21)\implies \begin{cases} 0=-x-9\implies &x=-9\\ 0=x-21\implies &21=x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \boxed{-9}\rule[0.35em]{8em}{0.25pt}0\rule[0.35em]{5em}{0.25pt}\stackrel{\downarrow }{6}\rule[0.35em]{10em}{0.25pt}\boxed{21}[/tex]
now, this parabolic graph, has two zeros/solutions/x-intercepts, at -9 and 21.
for a quadratic equation, the vertex will be right in between the x-intercepts, namely in this case between -9 and 21, right in the middle, namely at 6, and is where the axis of symmetry is at, x = 6.
Answer: The axis of symmetry is the line x = 6
The roots of the function f(x) are x = -9 and x = 21. They are found by setting f(x) equal to zero and solving for x. Each factor is set equal to zero by the zero product property and you solve each sub-equation
x+9 = 0 leads to x = -9
x-21 = 0 leads to x = 21
Average these two roots to get the midpoint. Add them up and divide by 2.
So we add the roots to get -9+21 = 12
Then we divide by two: 12/2 = 6
On a number line, if we had point A at -9 and point B at 21, then point C is the midpoint at 6.
The axis of symmetry is the vertical line that passes through the vertex of the parabola. It is the vertical mirror line of symmetry.
