Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10? –10, –12, –14, –16, –18, ... –2, 8, 18, 28, 38, .
2 answers:
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Answer: (2,2) and (-5,16)
Step-by-step explanation:
Here we have both Line (Linear Function) and Parabola (Quadratic Function)
So I am gonna write these equations here,
The first equation has Parabola graph (Since it's second degree.)
and the second equation has line graph.
To find the intersection, you have to substitute either -2x+6 in first equation (Quadratic) or x^2+x-4 in second equation (Linear)
For me, I am going to substitute x^2+x-4 in y=-2x+6.
Now solve the equation and find the value of x.
Since it's Quadratic Equation (Because there's x^2) I'd move -2x+6 to the left side.
Finish things here (Subtract and Addition)
What two numbers multiply to 10? Find the factors of 10, that are [1 and 10] and [2 and 5]
Now think about it, do you think that if 1 and 10 subtract or even addition, do you think that it'd be 3? No, of course not.
So 2 and 5 is right.
(5-2 = 3) and (5*(-2) = -10)
Then we get both x,
However, this is not it. You have to substitute both x in Linear Equation.
Substitute x = 2 in y=-2x+6
Order =
Then substitute x = -5 in y=-2x+6
Order =
So the intersections are both (2,2) and (-5,16) as shown in graph below.
