A bird flew down from a tree to grab a worm on the ground. The equation y=36.79x2−59.66x+24.19

represents the path of the bird, where x is time in seconds and y is the height above the ground in feet. Using the model, find the initial height of the bird in the tree. Round to the nearest tenth.(1 point)
Responses

36.8 feet
36.8 feet

24.2 feet
24.2 feet

0.8 feet
0.8 feet

24.1 feet

1 answer

To find the initial height of the bird in the tree, we need to evaluate the equation \( y = 36.79x^2 - 59.66x + 24.19 \) at \( x = 0 \) seconds (the initial time).

Let's substitute \( x = 0 \) into the equation:

\[ y = 36.79(0)^2 - 59.66(0) + 24.19 \]

Now, simplifying the equation:

\[ y = 0 - 0 + 24.19 \] \[ y = 24.19 \]

So, the initial height of the bird in the tree is \( 24.19 \) feet. Rounding to the nearest tenth gives us:

\[ 24.2 \text{ feet} \]

Thus, the correct response is \( \text{24.2 feet} \).