Determine the axis of symmetry for the function f(x) = −4(x + 7)2 − 3.

The equation of the axis of symmetry for is .

The function given in statement represents a parabola whose axis of symmetry is parallel to the y-axis. The standard form of the function is described below:

(1)

Where:

The equation for the axis of symmetry is of the form . By direct comparison, we determine that the equation of the axis of symmetry for is .

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  x = -7

Step-by-step explanation:

The vertex form of this equation tells us it is a downward-opening parabola with its vertex at (-7, -3). The line of symmetry is the vertical line through the vertex: x = -7.

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Vertex form is ...

  y = a(x -h) +k

where a is the vertical expansion factor, and (h, k) is the vertex. When a < 0, the parabola opens downward. When a > 0, it opens upward. (When a=0, the "parabola" is a horizontal line at y=k.)

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