QuestionFind the vertex of the function $f(x)=|x-4|+3$ . What are the coordinates of the vertex?

Studdy Solution

STEP 1

Assumptions1. The function is given by $f(x)=|x-4|+3$ . The vertex of a graph is the point where the graph reaches its maximum or minimum value.

STEP 2

The function $f(x)=|x-4|+$ is an absolute value function. The vertex of an absolute value function is the point at which the 'V' shape of the graph occurs. This point is determined by the values inside the absolute value function.

STEP 3

The vertex of the function $f(x)=|x-|+3$ is the point $(h, k)$ , where $h$ is the value that makes the expression inside the absolute value zero, and $k$ is the value of the function at $h$ .

STEP 4

To find the $x$ -coordinate of the vertex, set the expression inside the absolute value equal to zero and solve for $x$ .
$x -4 =0$

STEP 5

olving the equation $x -4 =0$ gives $x =4$ . So, the $x$ -coordinate of the vertex is $4$ .

STEP 6

To find the $y$ -coordinate of the vertex, substitute the $x$ -coordinate of the vertex into the function.
$f(4) = |4 -4| +3$

STEP 7

olving the equation $f(4) = |4 -4| +3$ gives $f(4) =3$ . So, the $y$ -coordinate of the vertex is $3$ .
Therefore, the vertex of the function $f(x)=|x-4|+3$ is at $(4,3)$ .

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QuestionFind the vertex of the function $f(x)=|x-4|+3$ . What are the coordinates of the vertex?

Studdy Solution

STEP 1

Assumptions1. The function is given by $f(x)=|x-4|+3$ . The vertex of a graph is the point where the graph reaches its maximum or minimum value.

STEP 2

The function $f(x)=|x-4|+$ is an absolute value function. The vertex of an absolute value function is the point at which the 'V' shape of the graph occurs. This point is determined by the values inside the absolute value function.

STEP 3

The vertex of the function $f(x)=|x-|+3$ is the point $(h, k)$ , where $h$ is the value that makes the expression inside the absolute value zero, and $k$ is the value of the function at $h$ .

STEP 4

To find the $x$ -coordinate of the vertex, set the expression inside the absolute value equal to zero and solve for $x$ .
$x -4 =0$

STEP 5

olving the equation $x -4 =0$ gives $x =4$ . So, the $x$ -coordinate of the vertex is $4$ .

STEP 6

To find the $y$ -coordinate of the vertex, substitute the $x$ -coordinate of the vertex into the function.
$f(4) = |4 -4| +3$

STEP 7

olving the equation $f(4) = |4 -4| +3$ gives $f(4) =3$ . So, the $y$ -coordinate of the vertex is $3$ .
Therefore, the vertex of the function $f(x)=|x-4|+3$ is at $(4,3)$ .

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QuestionFind the vertex of the function f(x)=∣x−4∣+3f(x)=|x-4|+3f(x)=∣x−4∣+3. What are the coordinates of the vertex?

Studdy Solution

STEP 1

Assumptions1. The function is given by f(x)=∣x−4∣+3f(x)=|x-4|+3f(x)=∣x−4∣+3 . The vertex of a graph is the point where the graph reaches its maximum or minimum value.

STEP 2

The function f(x)=∣x−4∣+f(x)=|x-4|+f(x)=∣x−4∣+ is an absolute value function. The vertex of an absolute value function is the point at which the 'V' shape of the graph occurs. This point is determined by the values inside the absolute value function.

STEP 3

The vertex of the function f(x)=∣x−∣+3f(x)=|x-|+3f(x)=∣x−∣+3 is the point (h,k)(h, k)(h,k), where hhh is the value that makes the expression inside the absolute value zero, and kkk is the value of the function at hhh.

STEP 4

To find the xxx-coordinate of the vertex, set the expression inside the absolute value equal to zero and solve for xxx.x−4=0x -4 =0x−4=0

STEP 5

olving the equation x−4=0x -4 =0x−4=0 gives x=4x =4x=4. So, the xxx-coordinate of the vertex is 444.

STEP 6

To find the yyy-coordinate of the vertex, substitute the xxx-coordinate of the vertex into the function.f(4)=∣4−4∣+3f(4) = |4 -4| +3f(4)=∣4−4∣+3

STEP 7

olving the equation f(4)=∣4−4∣+3f(4) = |4 -4| +3f(4)=∣4−4∣+3 gives f(4)=3f(4) =3f(4)=3. So, the yyy-coordinate of the vertex is 333.Therefore, the vertex of the function f(x)=∣x−4∣+3f(x)=|x-4|+3f(x)=∣x−4∣+3 is at (4,3)(4,3)(4,3).

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QuestionFind the vertex of the function $f(x)=|x-4|+3$ . What are the coordinates of the vertex?

Assumptions1. The function is given by $f(x)=|x-4|+3$ . The vertex of a graph is the point where the graph reaches its maximum or minimum value.

The function $f(x)=|x-4|+$ is an absolute value function. The vertex of an absolute value function is the point at which the 'V' shape of the graph occurs. This point is determined by the values inside the absolute value function.

The vertex of the function $f(x)=|x-|+3$ is the point $(h, k)$ , where $h$ is the value that makes the expression inside the absolute value zero, and $k$ is the value of the function at $h$ .

To find the $x$ -coordinate of the vertex, set the expression inside the absolute value equal to zero and solve for $x$ .
$x -4 =0$

olving the equation $x -4 =0$ gives $x =4$ . So, the $x$ -coordinate of the vertex is $4$ .

To find the $y$ -coordinate of the vertex, substitute the $x$ -coordinate of the vertex into the function.
$f(4) = |4 -4| +3$

olving the equation $f(4) = |4 -4| +3$ gives $f(4) =3$ . So, the $y$ -coordinate of the vertex is $3$ .
Therefore, the vertex of the function $f(x)=|x-4|+3$ is at $(4,3)$ .