To write the given quadratic equation to its vertex form, we first form a perfect square.
x² - 2x + 5 = 0
Transpose the constant to other side of the equation,
x² - 2x = -5
Complete the square in the left side of the equation,
x² - 2x + (-2/1(2))² = -5 + (-2/1(2))²
Performed the operation,
x² - 2x + 1 = -5 + 1
Factor the left side of the equation,
(x - 1)² = -4
Thus, the vertex form of the equation is,
<em> (x-1)² + 4 = 0</em>
X= r-h/y
h= xy-r/-1
r= xy+h
For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}
<h3>
How to get the domain and range?</h3>
Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:
x - 7 ≥ 0.
Solving for x we get:
x ≥ 0 + 7
Then the domain is:
x ≥ 7
To get the range, we evaluate in the minimum of the domain:
f(7) = √(7 - 7) + 9 = 9
Then the range is the set of all values larger than 9, because the function is increasing.
So the range is R: y ≥ 9.
If you want to learn more about domain and range:
brainly.com/question/10197594
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20
20 = 1 x 20
100 = 5 x 20
Answer:
It's 22.5 inches because the breadth is grater than the length
