# Write the equation in vertex form equivalent to f(x) = x^{2} + x +1?

**Solution:**

Vertex form of a quadratic equation refers to (x - h)^{2} = 4a (y - k) form or (y - k)^{2} = 4a (x - h) form depending on whether the square is on x-term or y-term respectively.

Given quadratic function is y = f(x) = x^{2} + x +1

In the given equation square term is for x.

∴ Equation must be reduced to (x - h)^{2} = 4a (y - k) form.

We have y = x^{2} + x + 1

⇒ y = x^{2} + x + 1 + 1/4 - 1/4 [by completing the square]

⇒ y = x^{2} + x + 1/4 + 3/4

⇒ y - 3/4 = (x + 1/2)^{2}

⇒ (x + 1/2)^{2} = y - 3/4

The above equation is in the vertex form.

## Write the equation in vertex form equivalent to f(x) = x^{2} + x +1?

**Summary:**

The vertex form of the given quadratic function, f(x) = x^{2} + x + 1, is (x + 1/2)^{2} = y - 3/4.

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