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Given the functions f(x) = 4x2 − 1, g(x) = x2 − 8x + 5, and h(x) = –3x2 − 12x + 1, rank them from least to greatest based on their axis of symmetry. g(x), h(x), f(x) f(x), h(x), g(x) g(x), f(x), h(x) h(x), f(x), g(x)

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The axis of symmetry of a quadratic function \(f(x)=ax^2+bx+c\) is given by the equation \(x=h\), where h is the x-coordinate of the vertex and is equal to \(\frac{-b}{2a}\).

1.
\(f(x)=4x^2-1 \\ a=4 \\ b=0 \\ \Downarrow \\ h=\frac{-0}{2 \times 4}=0 \\ \\ \hbox{the axis of symmetry:} \\ x=0\)

2.
\(g(x)=x^2-8x+5 \\ a=1 \\ b=-8 \\ \Downarrow \\ h=\frac{-(-8)}{2 \times 1}=\frac{8}{2}=4 \\ \\ \hbox{the axis of symmetry:} \\ x=4\)

3.
\(h(x)=-3x^2-12x+1 \\ a=-3 \\ b=-12 \\ \Downarrow \\ h=\frac{-(-12)}{2 \times (-3)}=\frac{12}{-6}=-2 \\ \\ \hbox{the axis of symmetry: \\ x=-2\)

The functions ranked from least to greatest based on their axis of symmetry: h(x), f(x), g(x).

cwcurfm180

Answer:

h(x) f(x) g(x)

Step-by-step explanation:

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