# `f(x) = x^2 ` f(x) - vertex (0,0), goes thru points (2,4), (-2,4) g(x) - vertex (2, -6), goes thru points (3,-3), (4,6) Which equation matches g(x)? a) `(3(x-2))^2 - 6` b)`(1/3(x-2))^2 -...

`f(x) = x^2 `

f(x) - vertex (0,0), goes thru points (2,4), (-2,4)

g(x) - vertex (2, -6), goes thru points (3,-3), (4,6)

Which equation matches g(x)?

a) `(3(x-2))^2 - 6`

b)`(1/3(x-2))^2 - 6`

c) `(3(x+2))^2 - 6`

d) `(1/3(x+2))^2 - 6`

e) `3(x+2)^2 - 6`

f) `3(x-2)^2 - 6`

g) `1/3(x+2)^2 - 6`

h) `1/3(x-2)^2 - 6`

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Expert Answers

lemjay | Certified Educator

To determine the equation of g(x), apply the vertex form of a parabola which is:

`y = a(x-h)^2+ k`

Then, plug-in the vertex of g(x).

`y = a(x-2)^2 - 6`

To determine the value of a, plug-in the other points of g(x). Use (3,-3).

`-3=a(3-2)^2-6`

`-3=a(1)^2-6`

`-3=a-6`

`-3+6=a-6+6`

`3=a`

**Hence, `g(x) = 3(x-2)^2-6` .**