Question

compare the graphs of the functions listed below.
function 1: $y = 0.25x^2$
function 2: $y = 4x^2$
function 3: $y = -\frac{1}{2}x^2$
function 4: $y = -16x^2$
the graph of is the widest.
done
function 1
function 2
function 3
function 4

Explanation:

Step1: Recall parabola width rule

For \( y = ax^2 \), \( |a| \) determines width. Smaller \( |a| \) means wider graph.

Step2: Calculate absolute values

• Function 1: \( |0.25| = 0.25 \)
• Function 2: \( |4| = 4 \)
• Function 3: \( |-\frac{1}{2}| = 0.5 \)
• Function 4: \( |-16| = 16 \)

Step3: Compare absolute values

\( 0.25 < 0.5 < 4 < 16 \), so function 1 has smallest \( |a| \).

Answer:

function 1