Question

Find the vertex

f(x)=3-|x+5|

Answer 1

vertex = (- 5, 3 )

Explanation:

to find the x- coordinate of the vertex, set the expression inside the function to zero.

x + 5 = 0 ( subtract 5 from both sides )

x = - 5

substitute x = - 5 into f(x) for y- coordinate

f(- 5) = 3 - | - 5 + 5 | = 3 - | 0 | = 3 - 0 = 3

vertex = (- 5, 3 )

Answer 2

• The vertex is (- 5, 3)

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Given

Absolute value function:

• f(x) = 3 - | x + 5 |

To find

• Vertex of the function

Solution

General form of absolute value function is:

• f(x) = a| x - h | + k, where (h, k) is its vertex.

Comparing with the given function, we have:

• a = -1, h = - 5, k = 3

So the vertex is:

• (- 5, 3)