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

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: