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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?
a.) Penelope should have subtracted 1 from both sides instead of adding 1.
b.) Penelope should have subtracted 4 from both sides instead of adding 1.
c.) Penelope should have added 4 to both sides instead of adding 1.
d.) Penelope should have subtracted 8 from both sides instead of adding 1.

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ANSWER

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

EXPLANATION

Penelope want to complete the square for

[tex]f(x)= 4 {x}^{2} + 8x + 1[/tex]
Penelope first of all equated the function to zero and added -1 to both sides to get,

[tex] - 1= 4 {x}^{2} + 8x [/tex]

Next Penelope factored 4 out of the right hand side of the equation to get,

[tex] - 1= 4( {x}^{2} + 2x )[/tex]

Next Penelope needs to add half the coefficient of x multiplied by a factor of 4 to both sides to obtain,

[tex] - 1 + 4= 4( {x}^{2} + 2x + 1)[/tex]

But Penelope rather made a mistake and added 1.

Therefore the correct answer is C.

Quadratic equation is the polynomial equation in which the there is only one unknown variable present. The highest power of the quadratic equation is two. The option C is the correct option as, Penelope should have added 4 to both sides instead of adding 1.

Given information-

The quadratic equation given in the problem is,

[tex]f(x) = 4x^2 + 8x + 1[/tex]

Quadratic equation

Quadratic equation is the polynomial equation in which the there is only one unknown variable present. The highest power of the quadratic equation is two.

To solve the above equation, equate it to the zero,

[tex]0= 4x^2 + 8x + 1[/tex]

Substract both side by one,

[tex]-1= 4x^2 + 8x [/tex]

[tex]-1= 4(x^2 + 2x )[/tex]

Substract with 4 from both sides,

[tex]\begin{aligned}\\ -1+4&= 4(x^2 + 2x )+4\\ 3&=4(x^2+2x+1)\\ \dfrac{3}{4} &=(x+2)^2\\ \dfrac{3}{4} &=x+2\\ \dfrac{3}{4} -2&=x\\ \dfrac{11}{4}& =x\\ \end[/tex]

The roots of x are 11/4 and 11/4.

Compare the above process with the process done Penelope to solve the quadratic equation, it concluded that he should add 4 both sides instead of adding 1.

Hence, the option C is the correct option as, Penelope should have added 4 to both sides instead of adding 1.

Learn more about the quadratic equation here;

https://brainly.com/question/17177510

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