Question

Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = –9(x + 1)2 – 7 g(x) = 4(x – 3)2 + 1 g(x) = –3(x – 4)2 – 6 g(x) = 8(x – 3)2 – 5

Answer 1

Choice D

Explanation:

Took the test

Answer 2

`g(x) = 8\cdot (x-3)^(2)-5`

Explanation:

Given that parent function represents a parabola, the standard form with a vertex at (h,k) is now described:

`y-k = C\cdot (x-h)^(2)`

`y = C \cdot (x-h)^(2) + k`

Where:

`x`,
`y` - Independent and dependent variables, dimensionless.

`h`,
`k` - Horizontal and vertical component of the vertex, dimensionless.

`C` - Vertex factor, dimensionless. (If C > 0, then vertex is an absolute minimum, but if C < 0, there is an absolute maximum).

After reading the statement of the problem, the following conclusion are found:

1) New function must have an absolute minimum:
`C > 0`

2) Transformation to the right:
`h > 0`.

3) Transformation downwards:
`k < 0`

Hence, the right choice must be
`g(x) = 8\cdot (x-3)^(2)-5`.