An owl swoops down from its perch in a tree at 20 feet to catch field mice below. It follows the function h = -6t² - 24t + 20. Plot points to graph the equation. Which ordered pair represents the vertex?
• (-2,44)
• (1,0)
• (-5,0)
• (44,-2
To find the vertex of the parabola represented by the equation h = -6t² - 24t + 20, we need to determine the values of t and h when the parabola reaches its maximum or minimum point.
Since the coefficient of t² is negative (-6), the parabola opens downward and the maximum point represents the vertex.
The x-coordinate of the vertex can be found using the formula:
t = -b / (2a),
where a = -6 and b = -24.
Substituting these values, we have:
t = -(-24) / (2(-6)) = 24 / 12 = 2.
To find the y-coordinate of the vertex, substitute the value of t (2) back into the equation:
h = -6(2)² - 24(2) + 20 = -6(4) - 48 + 20 = -24 - 48 + 20 = -52.
Therefore, the vertex of the parabola is (2, -52).
None of the given ordered pairs represents the vertex.