What is the vertex of the graph of y = 3x² + 2x + 1?

Solution:

We have to find the vertex of the graph.

For any equation of the type y = ax² + bx + c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is f(x) = 3x² + 2x + 1

Here, a = 3, b = 2 and c = 1

So, h = -2/2(3)

h = -2/6

h = -1/3

4ac = 4(3)(1)

4ac = 12

So, k = [12 - (2)²]/4(3)

k = (12 - 4)/12

k = 8/12

k = 2/3

Therefore, the vertex is (h, k) = (-1/3, 2/3).

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What is the vertex of the graph of y = 3x² + 2x + 1?

Summary:

The vertex of the graph f(x) = 3x² + 2x + 1 is (-1/3, 2/3).