The table represents the path of a boomerang as it leaves a person’s hand and comes back to their feet. Using technology, create an equation to model the situation. Round all values to the nearest hundredth.

Question

(1 point)
Responses

y=−3.83x2+21.14x−4.84
y equals negative 3.83 x squared plus 21.14 x minus 4.84

(x−2.49)=0.00(y−16.56)2
left parenthesis x minus 2.49 right parenthesis equals 0.00 left parenthesis y minus 16.56 right parenthesis squared

(x−24.73)=−3.83(y−2.76)2
left parenthesis x minus 24.73 right parenthesis equals negative 3.83 left parenthesis y minus 2.76 right parenthesis squared

(x−24.35)=−3.46(y−2.67)2
left parenthesis x minus 24.35 right parenthesis equals negative 3.46 left parenthesis y minus 2.67 right parenthesis squared
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Answer 1

To model the path of a boomerang using a quadratic equation or another suitable form, let’s analyze the options provided.

Option 1 is a quadratic function in standard form:

• \( y = -3.83x^2 + 21.14x - 4.84 \)

This represents a parabola opening downwards (as the coefficient of \( x^2 \) is negative), which may correspond to the arc of the boomerang's flight.

The other options are variations of the vertex form of a parabola. They can also describe a parabolic trajectory but involve transformations based on their given vertex values.

To determine the best model:

• For a typical boomerang flight path, the downward-opening parabola (like option 1) may accurately represent how the boomerang would typically rise and then fall back to the ground.

As such, the most appropriate equation to model the situation, based on the context, is:

\( y = -3.83x^2 + 21.14x - 4.84 \)

If the question is to identify the best equation from the options given, select:

\( y = -3.83x^2 + 21.14x - 4.84 \)