Write the quadratic function in vertex form. y = x² + 4x + 7.

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 = x² + 4x + 7

In the given equation square term is for x.

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

We have y = x² + 4x + 7

⇒ y = x² + 4x + 4 - 4 + 7

⇒ y = (x + 2)² + 3

⇒ y - 3 = (x + 2)²

The above equation is in the vertex form.

Write the quadratic function in vertex form. y = x² + 4x + 7.

Summary:

The vertex form of the given quadratic function, y = x² - 2x + 5, is (x -1)2 = y - 4.