Answer:
Part 1) The domain of the quadratic function is the interval (-∞,∞)
Part 2) The range is the interval (-∞,1]
Step-by-step explanation:
we have
![f(x)=-x^2+14x-48](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B14x-48)
This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)
step 1
Find the domain
The domain of a function is the set of all possible values of x
The domain of the quadratic function is the interval
(-∞,∞)
All real numbers
step 2
Find the range
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
we have a vertical parabola open downward
The vertex is a maximum
Let
(h,k) the vertex of the parabola
so
The range is the interval
(-∞,k]
Find the vertex
![f(x)=-x^2+14x-48](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B14x-48)
Factor -1 the leading coefficient
![f(x)=-(x^2-14x)-48](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-14x%29-48)
Complete the square
![f(x)=-(x^2-14x+49)-48+49](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-14x%2B49%29-48%2B49)
![f(x)=-(x^2-14x+49)+1](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-14x%2B49%29%2B1)
Rewrite as perfect squares
![f(x)=-(x-7)^2+1](https://tex.z-dn.net/?f=f%28x%29%3D-%28x-7%29%5E2%2B1)
The vertex is the point (7,1)
therefore
The range is the interval
(-∞,1]
Answer:
the total number of blocks is 69
Step-by-step explanation:
the way you can find this is by counting all the outside blocks on the closest side (23) and multiplying it by the the width of the blocks on the right side (3)
Answer: Yes
Step-by-step explanation:
The reason on why it could form a triangle because 18 is the highest side in the triangle and if you have 2 of the smaller sides that are greater than the larger size then you could form a triangle and 13 and 6 equals to 19 so you could make a triangle hopes this helps and have a good day.
Answer:
141.4
Step-by-step explanation:
i think