Answer: The range is y ≥ 3.
Step-by-step explanation:
When we have an equation:
y = f(x)
The range is the set of the possible values of y.
In this case, we have:
y = f(x) = 2*x^2 - 20*x + 53
This is a quadratic equation, and the leading coefficient is positive. This means that the arms of the graph will open upwards.
Then the minimum value of y will be the vale at the vertex.
We know that for a quadratic equation of the form:
a*x^2 + b*x + c
The vertex is at:
x = -b/2a
Then in this case, the vertex will be at:
x = -(-20)/(2*2) = 20/4 = 5
Then the smallest value of this function will be:
f(5) = 2*5^2 - 20*5 + 53 = 3
This is the smallest value that y can take, and y can take any value greater than 3.
Then the range can be written as:
y ≥ 3.
