Question

Rank the following from least to greatest based on their axis of symmetry.

f(x) = 4x^2 − 1
g(x) = x^2 − 8x + 5
h(x) = –3x^2 − 12x + 1

A.) g(x), h(x), f(x)
B.) f(x), h(x), g(x)
C.) g(x), f(x), h(x)
D.) h(x), f(x), g(x)

Answer 1

Finding the axis of symmetry.
1) Identify a, b, and c in the equation
f(x) = 4x² - 1 ⇒ a = 4 ; b = 0 ; c = -1
g(x) = x² - 8x + 5 ⇒ a = 1 ; b = -8 ; c = 5
h(x) = -3x² - 12x + 1 ⇒ a = -3 ; b = -12 ; c = 1

2) Formula of the axis of symmetry
x = -b/2a
f(x) ⇒ x = -0/2(4) = 0
g(x) ⇒ x = -(-8)/2(1) = 8/2 = 4
h(x) ⇒ x = -(-12)/2(-3) = 12/-6 = -2

Rank from least to greaters: -2, 0, 4 ⇒ h(x) ; f(x) ; g(x) CHOICE D