Question

assuming all parabolas are of the form $y = ax^2 + bx + c$, drag and drop the graphs to match the appropriate a - value (if necessary).
$a = 1$
$a = -1$
$a = 0.25$

Explanation:

Step1: Recall parabola properties

For \( y = ax^2 + bx + c \), the sign of \( a \) determines direction (up if \( a>0 \), down if \( a<0 \)), and \( |a| \) determines width (larger \( |a| \) means narrower, smaller \( |a| \) means wider).

Step2: Analyze \( a = 1 \)

\( a = 1>0 \), so parabola opens up. It should be narrower than \( a = 0.25 \) (since \( 1>0.25 \)). The first graph (left) opens up and is relatively narrow, so match \( a = 1 \) to the left graph.

Step3: Analyze \( a = -1 \)

\( a = -1<0 \), so parabola opens down. The middle graph opens down, so match \( a = -1 \) to the middle graph.

Step4: Analyze \( a = 0.25 \)

\( a = 0.25>0 \), opens up. It should be wider than \( a = 1 \) (since \( 0.25<1 \)). The right graph opens up and is wider, so match \( a = 0.25 \) to the right graph.

Answer:

• \( a = 1 \): The Left Graph
• \( a = -1 \): The Middle Graph
• \( a = 0.25 \): The Right Graph