Find the vertex of the graph of the function. f(x) = 3x² - 18x + 24

Solution:

Given, f(x) = 3x² - 18x + 24

We have to find the vertex of the function.

To find the vertex of the function, we have to convert the given function in the form

f(x) = a(x - h)² + k  ------------------ (1)

Where, (h,k) is the vertex.

Here, f(x) = 3(x² - 6x) + 24

f(x) = 3(x² - 2 × 3 × x + 3² - 3²) + 24

f(x) = 3(x - 3)² - 27 + 24

f(x) = 3(x - 3)² - 3 --------------- (2)

Comparing (1) and (2),

h = 3

k = -3

So, (h,k) = (3, -3)

Therefore, the vertex is (3, -3).

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Find the vertex of the graph of the function. f(x) = 3x² - 18x + 24

Summary:

The  vertex of the graph of the function. f(x) = 3x² - 18x + 24 is (3, -3).