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The function's vertex is found at the function's highest or lowest point.

In this case it's the lowest point and can be read as $(-2,-4).$

b

For quadratic functions, the axis of symmetry always goes through the vertex. Read the $x$-coordinate of the vertex and you'll find the axis of symmetry.

The $x$-coordinate is $-2$ so the axis of symmetry is $x=-2.$

c

The function's zeros is where the value of the function is $0$, so the $x$-values when the curve intersects the $x$-axis.

The zeros are $x=-5$ and $x=1.$