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# Find the vertex of the graph of the function. f(x) = 3x^{2} - 18x + 24

**Solution:**

Given, f(x) = 3x^{2} - 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(x^{2} - 6x) + 24

f(x) = 3(x^{2} - 2 × 3 × x + 3^{2} - 3^{2}) + 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).

## Find the vertex of the graph of the function. f(x) = 3x^{2} - 18x + 24

**Summary:**

The vertex of the graph of the function. f(x) = 3x^{2} - 18x + 24 is (3, -3).

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