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

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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xero099 xero099 · Answer 2 · 2021-10-19T10:43:55+02:00

The equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

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:

[tex]f(x) -k = C\cdot (x-h)^{2}[/tex] (1)

Where:

[tex]C[/tex] - Vertex constant.
[tex]x[/tex] - Independent variable.
[tex]f(x)[/tex] - Dependent variable.
[tex]h, k[/tex] - Vertex coordinates.

The equation for the axis of symmetry is of the form [tex]x = h[/tex]. By direct comparison, we determine that the equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

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