Answer:
f(x) = 4( x + 3/2)^2
Step-by-step explanation:
F(x) =4 x^2 + 12x + 9
= 4 [ x^2 + 3x] + 9
Add (3/2)^2 - (3/2)^2 to the square bracket, we have:
4 [ x^2 + 3x+ (3/2)^2 - (3/2)^2] + 9
4[ (x + 3/2 )^2 - 9/4] + 9
4( x + 3/2)^2 - 9/4 ×4 + 9
4( x + 3/2)^2 - 9 + 9
4( x + 3/2)^2 +0
4( x + 3/2)^2
Note the (3/2)^2 - (3/2)^2 is decoded by dividing b by 2 and squaring it and then subtracting same. Look at the general equation of a circle given below
ax^2 + bx + c
To form a square expression we adopt (b/2)^2 - (b/2)^2 to the general equation provided a = 1;
To make a = 1; we had to factor out 4 from the coefficient of x; making perfect square is of concern when we have ax^2 + bx ; irrespective of 'c' or not.
This is usually referred to as method of completing the square in solving quadratic equation
Answer:
there isnt any picture so nobody can answer this
Step-by-step explanation:
This is a geometric series. The first payment represents the first term, a. The number of times he wants to pay back for subsequent payments represent the common ration, r. The first 30 payments represents the number of terms to use in finding the sum, n.
Hence, a = $ 200, n = 30 and r = 1.2.
The sum of a geometric sequence is given as:
Sn = (a((r^n)-1))/(r-1)
=<span>(200((1.2^30)-1))/(1.2-1)
= $ 236, 376. 31
</span><span>Explain why this series is convergent or divergent.
</span>Since the common ratio, r, is greater than 1, the series is divergent