Answer:
Choice A. [tex]F(x) = -(x - 4)^{2} -3[/tex].
Step-by-step explanation:
Both F(x) and G(x) are quadratic equations. The graphs of the two functions are known as parabolas. All four choices for the equation of F(x) are written in their vertex form. That is:
[tex]y = a(x - h)^{2} + k[/tex], [tex]a \ne 0[/tex]
where
- The point [tex](h, k)[/tex] is the vertex of the parabola, and
- The value of [tex]a[/tex] determines the width and the direction of the opening of the parabola. [tex]a >0[/tex] means that the parabola opens upward. [tex]a <0[/tex] means that the parabola opens downwards. The opening becomes narrower if the value of [tex]a[/tex] increases.
For the parabola G(x),
- the vertex is at the point [tex](4, -3)[/tex], and
- the parabola opens downwards.
In other words,
- [tex]h = 4[/tex],
- [tex]k = -3[/tex], and
- [tex]a \le 0[/tex].
Hence choice A. [tex]F(x) = -(x - 4)^{2} -3[/tex].
