Hi, I need help finding the domain and range of the Quadratic Model on part b. I've included part a. just in case you may need it.
a.The parabolic path of a thrown ball can be modeled by the table. the top of the wall is at (5,6). Will the ball go over the wall? If not,will it hit wall on the way up, or the way down?
b. what is the reasonable domain and range for the function that models the path of the ball?
X:1,2,3
Y:3,5,6
How do I find the domain and range not only in this but other problems too? My book says the answer is: Domain:0 is less than or equal to x, x is less than or equal to 7. Range: 0 is less than or equal to y,y is less than or equal to 6 1/8.
y = a + b x^2
3 = a + b (1)^2 = a + b
5 = a + b(2)^2 = a + 4 b
b = 3 - a
5 = a + 4(3-a)
5 = a + 12 - 4a
3 a = 7
a = 7/3
b = 9/3 - 7/3 = 2/3
so
y =7/3 +2/3 x^2
check last point
y = 7/3 + (2/3)(9) = 7 1/3
I do not think your table is a parabola
well, maybe
y = a + b x + c x^2
3 = a + b(1) + c(1)
5 = a + b(2) + c(4)
6 = a + b(3) + c(9)
so
2 = b + 3 c
1 = b + 5 c
----------
1 = -2c
c = -1/2
1 = b -5/2
b = 7/2
3 = a + 7/2 -1/2 = a + 3 so a = 0
y = 0 + 7 x/2 - x^2/2
y = (7/2) x - (1/2)x^2
or
2 y = 7 x - x^2
y = (7/2) x - (1/2)x^2
reasonable domain is above ground, y>0 so
solve for zeros of x
x^2 -7x = 0
x = 0 to x = 7
range (vertex is when x = half 7 or3.5
ymax = (7/2)(7/2) -(1/2)(7/2)^2
= (1/2)(49/4) = 49/8 = 6.125
so range is 0 to 6.125
Now that point (5,6)
5 is beyond x = 3.5 so on the way down
y = (7/2)(5)- (1/2)(25)
= 10/2 = 5
will not make it over wall
To find the domain and range of a function, such as the quadratic model that represents the ball's path, you need to consider the set of possible input values (domain) and the corresponding output values (range).
In this case, let's analyze the given quadratic model represented by the table:
X: 1, 2, 3
Y: 3, 5, 6
To determine the domain, we need to identify all possible x-values. In this case, the x-values are given as 1, 2, and 3. Therefore, the domain consists of these values: {1, 2, 3}.
Now, let's look at the range. The range refers to the set of possible y-values. In this case, the y-values are given as 3, 5, and 6. Therefore, the range consists of these values: {3, 5, 6}.
However, the answer provided in your book seems to be different. According to the answer you've mentioned, the domain is "0 is less than or equal to x, x is less than or equal to 7," and the range is "0 is less than or equal to y, y is less than or equal to 6 1/8."
To help you understand how the book arrived at this answer, we would need more information or context. Could you provide any additional details from the book or the problem statement?