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2 years ago

Determine the Vertex of the following absolute value function.

Mathematics

1 answer:

prisoha [69]2 years ago

6 0

Answer:

vertex = (-4, 5)

Step-by-step explanation:

In general, the graph of the absolute value function f(x) = a|x - h| + k will have its lowest value when f(x) = k (or highest value for f(x) = -a|x - h| + k). The lowest/highest value is the vertex (turning point).

Therefore, from inspection of the equation we can say that the y-coordinate of the vertex is 5.

Set the equation to 5 and then solve for x:

⇒ 5 = 1/2 |-X – 4| + 5

⇒ 1/2 |-X – 4| = 0

⇒ |-X – 4| = 0

Therefore, (-X - 4) = 0 and -(-X - 4) = 0

⇒ X = -4 (for both)

So the vertex is (-4, 5)

Translations

Absolute value parent function: f(x) = | -x |

Horizontal translation left 4 units: f(x) = |-x - 4|

Horizontal stretch of sf 1/2: f(x) = 1/2 |-x - 4|

Vertical translation up 5 units: f(x) = 1/2 |-x - 4| + 5

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kap26 [50]

Answer:

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Step-by-step explanation:

Hi there,

In order to find the length of side EF, you should realize that this is an isosceles triangle. We know that two sides and two angles of this type of triangle are equal to each other. We also know that the lengths of the sides opposite of the congruent angles are equal to each other. Thus, we proved that length of side EF is equal to the length of side FG.

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2 years ago

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Sonja [21]

Answer:

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Step-by-step explanation:

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