To interpret the vertex of the function \( h = 6t^2 - 24t + 30 \) correctly, we first need to find the vertex of this quadratic function.
The vertex of a quadratic function in the form of \( h = at^2 + bt + c \) can be calculated using the formula for the \( t \)-coordinate of the vertex:
\[ t = -\frac{b}{2a} \]
In your equation:
- \( a = 6 \)
- \( b = -24 \)
Now, substituting the values in:
\[ t = -\frac{-24}{2(6)} = \frac{24}{12} = 2 \]
Next, we calculate the corresponding \( h \) value by substituting \( t = 2 \) back into the function:
\[ h = 6(2)^2 - 24(2) + 30 \] \[ = 6(4) - 48 + 30 \] \[ = 24 - 48 + 30 \] \[ = 6 \]
Thus, the vertex is \( (2, 6) \).
Interpretation of the vertex: The vertex \( (2, 6) \) represents the minimum height of the owl during its dive, which occurs at \( t = 2 \) seconds, with a height of 6 feet.
From the responses you provided, the correct answer is:
(2, 6).
1 answer