ANSWER
The other zero is
[tex]x = - 10[/tex]
EXPLANATION
The axis of symmetry serves as the midpoint of the two zeroes.
We were given that the axis of symmetry of the quadratic equation is
[tex]x = - 3[/tex]
We were also given that, one of the zeroes of the quadratic equation is
[tex]x = 4[/tex]
Let the other zero of the quadratic equation be
[tex]x = p[/tex]
,then, we apply the midpoint formula to find the value of
[tex]p[/tex]
Since it is the x-values of the intercepts that gives the solution, we use only the x-value part of the midpoint formula which is given by,
[tex] \frac{x_1 + x_2}{2} = axis \: of \: symmetry[/tex]
We substitute to obtain,
[tex] \frac{p + 4}{2} = - 3[/tex]
We multiply through by 2 to get,
[tex] p + 4 = - 6[/tex]
This implies that,
[tex]p = - 6 - 4[/tex]
[tex]p = - 10[/tex]
