Answer:
he rank from least to great based on their axis of symmetry:
0, 1, -3 ⇒ g(x), h(x), f(x)
So, option C is correct.
Step-by-step explanation:
A quadratic equation is given by:
[tex]ax^2+bx+c =0[/tex]
Here, a, b and c are termed as coefficients and x being the variable.
Axis of symmetry can be obtained using the formula
[tex]x = \frac{-b}{2a}[/tex]
Identification of a, b and c in f(x), g(x) and h(x) can be obtained as follows:
[tex]f(x) = x^2 + 6x - 1[/tex]
⇒ a = 1, b = 6 and c = -1
[tex]g(x) = -x^2 + 2[/tex]
⇒ a = -1, b = 0 and c = 2
[tex]h(x) = 2^2 - 4x + 3[/tex]
⇒ a = 2, b = -4 and c = 3
So, axis of symmetry in [tex]f(x) = x^2 + 6x - 1[/tex] will be:
[tex]x = \frac{-b}{2a}[/tex]
x = -6/2(1) = -3
and axis of symmetry in [tex]g(x) = -x^2 + 2[/tex] will be:
[tex]x = \frac{-b}{2a}[/tex]
x = -(0)/2(-1) = 0
and axis of symmetry in [tex]h(x) = 2^2 - 4x + 3[/tex] will be:
[tex]x = \frac{-b}{2a}[/tex]
x = -(-4)/2(2) = 1
So, the rank from least to great based on their axis of symmetry:
0, 1, -3 ⇒ g(x), h(x), f(x)
So, option C is correct.
Keywords: axis of symmetry, functions
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