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Answer:
Answers are in bold type
Step-by-step explanation:
f(x) =
The parabola opens up, so has a minimum at the vertex.
Let (h, k) be the vertex
h = -b/2a = - (-144)/2(1) = 57
k = 57^2 - 144(57) = 3249 - 6498 = -3249
Therefore, the vertex is (57, -3249)
The minimum value is -3249
The domain is the set of real numbers.
The range = {y | y ≥ -3249}
The function decreases when -∞ < x < 57 and increases when 57 > x > ∞
The x - intercepts: = 0
x(x - 114x) = 0
x = 0 or x = 114
x-intercepts are (0, 0) and (0, 114)
When x = 0, then we get the y-intercept. So, 0^2 - 114(0) = 0
y-intercept is (0, 0)
<h3>The base area of triangular prism container is 42.8 cubic centimeter</h3>
<em><u>Solution:</u></em>
<em><u>The volume of triangular prism is given as:</u></em>
Given that,
A triangular prism container is full of water of 428 cubic cm
The water is 10 cm deep
Therefore,
v = 428 cubic cm
h = 10 cm
<em><u>Substituting the values we get,</u></em>
Thus the base area of triangular prism container is 42.8 cubic centimeter