The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown. f(x) = 4(x2 + 12x) + 10 = 36 what is the function written in vertex form? f(x) = 4(x + 6)2 + 10 f(x) = 4(x + 6)2 – 26 f(x) = 4(x + 6)2 – 134 f(x) = 4(x + 6)2 + 154

f(x) = 4(x + 6)² – 134

Step-by-step explanation:

To write an equation in vertex form, we first factor out the GCF of the first two terms.  For 4x² and 48x, this is 4:

f(x) = 4(x²+12x)+10

Next we complete the square.  The value of b inside parentheses is 12; we take half of that and square it:

(12/2)² = 6² = 36

We add this inside parentheses.  However in order to preserve equality, we must subtract this value as well.  Since the terms inside parentheses are being multiplied by 4, we multiply the 36 we subtract by 4 as well:

f(x) = 4(x²+12x+36)-4(36)+10

Simplifying, we have

f(x) = 4(x²+12x+36)-144+10

Combining like terms,

f(x) = 4(x²+12x+36)-134

Next we write the trinomial in parentheses as a perfect square:

f(x) = 4(x+6)²-134

its C

Step-by-step explanation:

edge 2020

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}