The graph of a quadratic function has roots at - 3 and - 7 and a vertex at (-5, 4). What is the equation of the function in vertex form?

y = - (x + 5) ² + 4

Step-by-step explanation:

The roots are - 3 and - 7, so:

y = a (x + 3) (x + 7)

Distribute and complete the square:

y = a (x² + 10x + 21)

y = a (x² + 10x + 25 - 4)

y = a (x² + 10x + 25) - 4a

y = a (x + 5) ² - 4a

The vertex is (-5, 4), so a = - 1.

y = - (x + 5) ² + 4