How do you find the vertex of a quadratic function? Find the vertex of quadratic function y = x² + 2x - 2 .

We will use the concept of differentiation in order to find the vertex of a quadratic function.

Answer: The vertex of quadratic function y = x² + 2x - 2 is given by point (-1, -3)

Let us see how we will use the concept of differentiation in order to find the vertex of a quadratic function.

Explanation:

The point where a quadratic equation has a vertex is the point where dy / dx = 0.

Hence, let us calculate dy / dx for the quadratic function y = x² + 2x - 2.

On differentiating both sides we get,

dy / dx = 2x + 2.

Now substituting dy / dx = 0, we get

0 = 2x + 2

⇒ x = -1

Substitute x = -1 in y = x² + 2x - 2

y = x² + 2x - 2

y = (-1)² + 2(-1) - 2 = -3

ALTERNATE METHOD:

For quadratic equation y = ax² + bx + c, the x-coordinate of the vertex is given by -b/2a

For y = x² + 2x - 2, a = 1, b = 2, c = -2

⇒ x - coordinate of the vertex is -b/2a =. -2/2.1 = -1

Put x = -1 in y = x² + 2x - 2, we get y = -3

Thus, the coordinates of the vertex are x = -1 and y = -3.

Hence, point (-1, -3) is the vertex of the quadratic equation y = x² + 2x - 2.