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

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

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 squares4*(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.