Question

enelope 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.

Answer 1

Answer:

c Penelope should have added 4 to both sides instead of adding 1.

Step-by-step explanation:

Answer 2

The correct question is
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?

we have that
f(x) = 4x² + 8x + 1
to find the solutions of the quadratic function
let
f(x)=0
 4x² + 8x + 1=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

 (4x² + 8x)=-1

Factor the leading coefficient 

 4*(x² + 2x)=-1

Complete the square Remember to balance the equation by adding the same constants to each side.

 4*(x² + 2x+1)=-1+4 --------> ( added 4 to both sides)

Rewrite as perfect squares

4*(x+1)²=3

(x+1)²=3/4--------> (+/-)[x+1]=√3/2

(+)[x+1]=√3/2---> x1=(√3/2)-1----> x1=(√3-2)/2

(-)[x+1]=√3/2----> x2=(-2-√3)/2

therefore

the answer is

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