Answered

Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Join our interactive Q&A platform to receive prompt and accurate responses from experienced professionals in various fields.

Drag each label to the correct location on the table.

Match each equation with its number of unique solutions.

[tex]
y = 3x^2 - 6x + 3 \quad y = -x^2 - 4x + 7 \quad y = -2x^2 + 9x - 11
[/tex]

\begin{tabular}{|l|c|}
\hline
Two Real Solutions & One Real Solution \\
\hline
& \\
& \\
\hline
One Complex Solution & Two Complex Solutions \\
\hline
& \\
& \\
\end{tabular}

Sagot :

GinnyAnsweridn
To determine the number of unique solutions for each quadratic equation, we use the discriminant [tex]\( \Delta \)[/tex] given by the equation [tex]\(\Delta = b^2 - 4ac \)[/tex]. Here is the result for each equation:

1. For the equation [tex]\( y = 3x^2 - 6x + 3 \)[/tex]:
- The discriminant is zero, which means there is one real solution.
- So, this equation goes under "One Real Solution".

2. For the equation [tex]\( y = -x^2 - 4x + 7 \)[/tex]:
- The discriminant is positive, which means there are two real solutions.
- So, this equation goes under "Two Real Solutions".

3. For the equation [tex]\( y = -2x^2 + 9x - 11 \)[/tex]:
- The discriminant is negative, which means there are two complex solutions.
- So, this equation goes under "Two Complex Solutions".

Thus, the table will be filled as follows:

\begin{tabular}{|l|c|}
\hline Two Real Solutions & One Real Solution \\
\hline [tex]\( y = -x^2 - 4x + 7 \)[/tex] & [tex]\( y = 3x^2 - 6x + 3 \)[/tex] \\
& \\
\hline One Complex Solution & Two Complex Solutions \\
\hline & [tex]\( y = -2x^2 + 9x - 11 \)[/tex] \\
& \\
& \\
& \\
& \\
& \\
& \\
& \\
&
\end{tabular}
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.