Trying to factor by splitting the middle term
Factoring <span> b2-4b+4</span>
The first term is, <span> <span>b2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -4b </span> its coefficient is <span> -4 </span>.
The last term, "the constant", is <span> +4 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> 1 • 4 = 4</span>
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is <span> -4 </span>.
<span><span> </span></span>
<span><span>-4 + -1 = -5</span><span> -2 + -2 = -4 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -2
<span>b2 - 2b</span> - 2b - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
b • (b-2)
Add up the last 2 terms, pulling out common factors :
2 • (b-2)
Step-5 : Add up the four terms of step 4 :
(b-2) • (b-2)
Which is the desired factorization
Answer:
23.800
Step-by-step explanation:
Gradient = change in y /change in x so -6-2 =-8 / -16-4 = -20 so -8/-20 = 0.4 so gradient = 0.4
Answer:
The axis of symmetry is 
Step-by-step explanation:
we know that
In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex
In this problem we have a vertical parabola open upward
The x-coordinate of the vertex is equal to the midpoint between the zeros of the parabola
so

therefore
The axis of symmetry is 
Let

Differentiating twice gives


When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.
Substitute these into the given differential equation:


Then the coefficients in the power series solution are governed by the recurrence relation,

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.
• If n is even, then n = 2k for some integer k ≥ 0. Then




It should be easy enough to see that

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then




so that

So, the overall series solution is

