ANSWER
The other zero is
\(x = - 10\)
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
\(x = - 3\)
We were also given that, one of the zeroes of the quadratic equation is
\(x = 4\)
Let the other zero of the quadratic equation be
\(x = p\)
,then, we apply the midpoint formula to find the value of
\(p\)
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,
\(\frac{x_1 + x_2}{2} = axis \: of \: symmetry\)
We substitute to obtain,
\(\frac{p + 4}{2} = - 3\)
We multiply through by 2 to get,
\(p + 4 = - 6\)
This implies that,
\(p = - 6 - 4\)
\(p = - 10\)
