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3 years ago

Functions f(x) and g(x) are shown below:

Mathematics

1 answer:

kondor19780726 [428]3 years ago

4 0

We look for the minimum of each function.
For f (x) = 3x2 + 12x + 16:
We derive the function:
f '(x) = 6x + 12
We match zero:
6x + 12 = 0
We clear the value of x:
x = -12/6
x = -2
We substitute the value of x in the equation:
f (-2) = 3 * (- 2) ^ 2 + 12 * (- 2) + 16
f (-2) = 4
For g (x) = 2sin(x-pi):
From the graph we observe that the minimum value of the function is:
y = -2
Answer:
A function that has the smallest minimum y-value is:
y = -2

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Answer:

Horizontal translation of the parent graph

Step-by-step explanation:

<h2>Definitions:</h2>

In the vertex form of a quadratic function, f(x) = a(x - h)² + k, where:

(h, k) = vertex of the graph

a = determines the width and direction of the graph's opening.

A horizonal translation to the parent graph is given by, y = f(x - h), where:

h > 0 ⇒ Horizontal translation of h units to the right

h < 0 ⇒ Horizontal translation of |h | units to the left

In the graph of g(x) = (x + 12)², the vertex occurs at point (-12, 0).

While the vertex of the parent graph, f(x) = x² occurs at point, (0, 0).

<h2>Answers:</h2>

Since the vertex of g(x) occurs at point, (-12, 0), substituting the value of (h, k ) into the vertex form will result into:

g(x) = a(x - h)² + k

g(x) = [x - (-12)]² + 0

g(x) = (x + 12)² + 0

g(x) = (x + 12)²

Therefore, the graph of g(x) = (x + 12)² represents the horizontal translation of the parent graph, f(x) = x², where the graph of g(x) is horizontally translated 12 units to the left.

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What is the y-intercept?

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The y-intercept is 10.

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