Answered

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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}
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