What is the first step when rewriting y = -4x² + 2x - 7 in the form y = a(x - h)² + k?

Solution:

We will use the method of completing the square to rewrite the equation y = 6x² + 18x + 14 in the vertex form y = a(x - h)² + k.

Given : y = -4x² + 2x - 7. Our aim is to make the first two terms a perfect square trinomial.

Step 1: Take out -4 as common from first two terms,

y = -4(x² - 1/2 x) - 7

Step 2: Take the negative half of the coefficient of x, and square it

(1/4)²

Step 3: Add and subtract the number from the equation.

y = -4(x² - 1/2 x + (1/4)²) - 7+ [- 4(1/4)²] [Multiply by -4 taken out a common outside the bracket]

y = - 4[x - (1/4)]² - 7 - (-1/4)

y = -4[x - (1/4)]² - 29/4

The vertex form of the equation is -4[x - (1/4)]² - 29/4.

What is the first step when rewriting y = -4x² + 2x - 7 in the form y = a(x - h)² + k?

Summary:

The first step when rewriting y = -4x² + 2x - 7 in the form y = a(x - h)² + k is to make the first two terms as a perfect square trinomial by completing the square.