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A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# Write the quadratic function in vertex form y = x^{2} - 2x + 5.

**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 = x^{2} - 2x + 5

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} - 2x + 5

⇒ y = (x^{2} - 2x + 1) + 5 -1 [By completing the square]

⇒ y - 4 = (x -1)^{2}

⇒ (x -1)^{2} = y - 4

The above equation is in the vertex form.

## Write the quadratic function in vertex form y = x^{2} - 2x + 5.

**Summary:**

The vertex form of the given quadratic function, y = x^{2} - 2x + 5, is (x -1)^{2} = y - 4.

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