By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.
Any equation of the form [tex]ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .
Given work of Penelope is
[tex]$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+1=4\left(x^{2}+2 x+1\right) \\&0=4(x+2)^{2} \\&0=(x+2)^{2} \\&0=x+2 \\&-2=x\end{aligned}$[/tex]
Now we can see that Penelope determined the solutions of the quadratic function by completing the square. so he must have been done as following
[tex]$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+4=4\left(x^{2}+2 x+1\right) \\&3=4(x+2)^{2} \\&\frac{3}{4} =x+2)^{2} \\&\frac{\pm\sqrt3}{2} =x+2 \\&\frac{-2\pm\sqrt3}{2} =x\end{aligned}$[/tex]
By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.
To learn more about quadratic equations visit : https://brainly.com/question/1214333
Answer:
C) Penelope should have added 4 to both sides instead of adding 1.
Step-by-step explanation:
Got it right on edge! Good Luck <3
