Penelope determined the solutions of the quadratic function by completing the square.

f(x) = 4x2 + 8x + 1
–1 = 4x2 + 8x

–1 = 4(x2 + 2x)

–1 + 1 = 4(x2 + 2x + 1)

0 = 4(x + 2)2

0 = (x + 2)2

0 = x + 2

–2 = x

What error did Penelope make in her work?

Penelope should have subtracted 1 from both sides instead of adding 1.
Penelope should have subtracted 4 from both sides instead of adding 1.
Penelope should have added 4 to both sides instead of adding 1.
Penelope should have subtracted 8 from both sides instead of adding 1.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation:

not sure but it may be b, as i said i'm not sure.

my guess would be b and d, but i didn’t actually get out the pen and paper. lol