An owl swoops down from its perch in a tree at 30 feet to catch field mice. It follows the function h=6t2 −24t+30 , where t is the time in seconds and h is the height in feet. Which of the following best interprets the vertex?(1 point)
Responses
(2,6)
left parenthesis 2 comma 6 right parenthesis
(0,30)
left parenthesis 0 comma 30 right parenthesis
(30,0)
left parenthesis 30 comma 0 right parenthesis
(6,2)
The vertex of the quadratic function h=6t^2 - 24t + 30 represents the highest or lowest point on the graph of the function. In this case, since the owl is swooping down from its perch, the vertex represents the lowest point.
To find the vertex, we can use the formula t = -b/(2a), where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
In this case, a = 6 and b = -24. Plugging these values into the formula, we get:
t = -(-24)/(2(6))
t = 24/12
t = 2
Now we can substitute this value of t back into the equation to find h:
h = 6(2)^2 - 24(2) + 30
h = 24 - 48 + 30
h = 6
Therefore, the vertex is (2, 6). So the correct answer is:
(2,6)