Use the Mean Value Theorem to prove the inequality |sina − sinb| ≤ |a − b| for all
Real numbers a and b

y = - 3(x + 2)² + 12

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 2, 12), thus

y = a(x + 2)² + 12

To find a substitute (- 4, 0) into the equation

0 = a(- 2)² + 12, that is

4a + 12 = 0 ( subtract 12 from both sides )

4a = - 12 ( divide both sides by 4 )

a = - 3

y = - 3(x + 2)² + 12 ← equation in vertex form