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

Answer:

$g(x) = 8\cdot (x-3)^{2}-5$

Step-by-step 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 $g(x) = 8\cdot (x-3)^{2}-5$.

Answer 2

Answer:

Choice D

Step-by-step explanation:

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