Rachna purchases a plant that is 6 inches tall. Every week the plant grows an additional 0.6 inches. Rachna draws a graph of the
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seperable differential equations will have the form
what you do from here is isolate all the y terms on one side and all the X terms on the other
just divided G(y) to both sides and multiply dx to both sides
then integrate both sides
once you integrate, you will have a constant. use the initial value condition to solve for the constant, then try to isolate x or y if the question asks for it
In your problem,
so all you need to integrate is
Answer: Vertex = (2, -15) 2nd point = (0, -3)
<u>Step-by-step explanation:</u>
g(x) = 3x² - 12x - 3
= 3(x² - 4x - 1)
a=1 b=-4 c=-1
Find the x-value of the vertex by using the formula for the axis of symmetry:
= 2
Find the y-value of the vertex by plugging the x-value (above) into the given equation: g(x) = 3x² - 12x - 3
g(2) = 3(2)² - 12(2) - 3
= 12 - 24 - 3
= -15
So, the vertex is (2, -15) ← PLOT THIS COORDINATE
Now, choose a different x-value. Plug it into the equation and solve for y. <em>I chose x = 0</em>
g(0) = 3(0)² - 12(0) - 3
= 0 - 0 - 3
= -3
So, an additional point is (0, -3) ← PLOT THIS COORDINATE
The partial derivatives are not equal, so the equation is not exact.