Question

What is the vertex form of the equation y = x² + 8x + 15?

(a) y = (x + 4)² - 1
(b) y = (x - 4)² - 1
(c) y = (x + 8)² - 1
(d) y = (x - 8)² - 1

Answer 1

The vertex form of the equation y = x² + 8x + 15 is y = (x + 4)² - 1.

Step-by-step explanation:

The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola. To find the vertex form of the equation y = x² + 8x + 15, we need to complete the square. First, let's rewrite the equation as y = (x² + 8x) + 15. Next, we want to add and subtract the square of half the coefficient of x to complete the square. The coefficient of x is 8, so half of 8 is 4. Adding and subtracting 4² = 16, we get y = (x² + 8x + 16 - 16) + 15. We can rewrite this as y = (x + 4)² - 1. Therefore, the vertex form of the equation is y = (x + 4)² - 1.