Answer:
Option D) h(x), f(x), g(x)
Step-by-step explanation:
we know that
The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola
Part 1) we have
![f(x)=4x^{2} -1](https://tex.z-dn.net/?f=f%28x%29%3D4x%5E%7B2%7D%20-1)
This is a vertical parabola open upward
The vertex is a minimum The vertex is the point (0,-1)
The x-coordinate of the vertex is 0
so
The axis of symmetry is x=0
Part 2) we have
![g(x)=x^{2}-8x+5](https://tex.z-dn.net/?f=g%28x%29%3Dx%5E%7B2%7D-8x%2B5)
This is a vertical parabola open upward
The vertex is a minimum
Convert the equation into vertex form
![g(x)-5=x^{2}-8x](https://tex.z-dn.net/?f=g%28x%29-5%3Dx%5E%7B2%7D-8x)
![g(x)-5+16=x^{2}-8x+16](https://tex.z-dn.net/?f=g%28x%29-5%2B16%3Dx%5E%7B2%7D-8x%2B16)
![g(x)+11=x^{2}-8x+16](https://tex.z-dn.net/?f=g%28x%29%2B11%3Dx%5E%7B2%7D-8x%2B16)
![g(x)+11=(x-4)^{2}](https://tex.z-dn.net/?f=g%28x%29%2B11%3D%28x-4%29%5E%7B2%7D)
![g(x)=(x-4)^{2}-11](https://tex.z-dn.net/?f=g%28x%29%3D%28x-4%29%5E%7B2%7D-11)
The vertex is the point (4,-11)
The x-coordinate of the vertex is 4
so
The axis of symmetry is x=4
Part 3) we have
![h(x)=-3x^{2}-12x+1](https://tex.z-dn.net/?f=h%28x%29%3D-3x%5E%7B2%7D-12x%2B1)
This is a vertical parabola open downward
The vertex is a maximum
Convert the equation into vertex form
![h(x)-1=-3x^{2}-12x](https://tex.z-dn.net/?f=h%28x%29-1%3D-3x%5E%7B2%7D-12x)
![h(x)-1=-3(x^{2}+4x)](https://tex.z-dn.net/?f=h%28x%29-1%3D-3%28x%5E%7B2%7D%2B4x%29)
![h(x)-1-12=-3(x^{2}+4x+4)](https://tex.z-dn.net/?f=h%28x%29-1-12%3D-3%28x%5E%7B2%7D%2B4x%2B4%29)
![h(x)-13=-3(x+2)^{2}](https://tex.z-dn.net/?f=h%28x%29-13%3D-3%28x%2B2%29%5E%7B2%7D)
![h(x)=-3(x+2)^{2}+13](https://tex.z-dn.net/?f=h%28x%29%3D-3%28x%2B2%29%5E%7B2%7D%2B13)
The vertex is the point (-2,13)
The x-coordinate of the vertex is -2
so
The axis of symmetry is x=-2
Part 4) Rank their axis of symmetry from least to greatest
1) h(x) -----> axis of symmetry -2
2) f(x) -----> axis of symmetry 0
3) g(x) -----> axis of symmetry 4
so
h(x),f(x),g(x)