Answer:
f(x) = 2(x + 4)² - 2
Step-by-step explanation:
Equation of quadratic function whose vertex is (h, k),
f(x) = a(x - h)² + k
Equation of the function with vertex (-4, -2) shown in the graph will be,
f(x) = a(x + 4)² - 2
This graph is passing through a point (-6, 6) also,
6 = a(-6 + 4)² - 2
6 + 2 = a(-2)²
a = = 2
Therefore, quadratic function is f(x) = 2(x + 4)² - 2
Answer:
Step-by-step explanation:
We have a separable equation, first let's rewrite the equation as:
But:
So:
Multiplying both sides by dx and dividing both sides by 3a+y:
Integrating both sides:
Evaluating the integrals:
Where C1 is an arbitrary constant.
Solving for y:
So:
Finally, let's evaluate the initial condition in order to find C1:
Solving for C1:
Therefore: