Question

Can someone pls help

Answer 1

Y-k = a(x-h)²; h and k are given vertex(0,3), then

y -3 = a(x-0)²→ y = ax² + 3. From the table we can calculate a:(for x =1, y=2)

2 =a(1²) +3→ 2= a + 3 and a = -1, hence the equation:

y = -x². It's a parabola open downward with a max at (0,3)

y' = - 2x: This is the equation of the tangent with a rate of change = -2

Another way:
For x = 8, y₁'= -16. For x = 9, y₂' = -18

y'₂ - y'₁ = -18 + 16→ rate of change = -2