Write the quadratic function f(x) = x² + 8x + 3 in vertex form.

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 f(x) = x² + 8x + 3

In the given equation square term is for x.

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

We have y = f(x) = x² + 8x + 3

⇒ y = (x² + 8x +16) -16 + 3 [by completing the square]

⇒ y = (x + 4)² -13

⇒ y + 13 = (x + 4)²

⇒ (x + 4)² = y +13

The above equation is in the vertex form.

Write the quadratic function f(x) = x² + 8x + 3 in vertex form.

Summary:

The vertex form of the given quadratic function, f(x) = x² + 8x + 3, is (x + 4)² = y +13.