The equation of g in the form y = ax² + bx +c is g(x) = x² - 10x + 26
What is a function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Horizontal translation:
For a general function f(x) an horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the shift is to the left
If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x) a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive, the shift is upwards
If N is negative, the shift is downwards.
First, we apply a translation to the right of 5 units, then at the moment we have:
g(x) = f(x - 5)
Then we translate the graph up 1 units, then:
g(x) = f(x - 5) + 1
Now we can replace it by the actual function to get:
g(x) = (x - 5)^2 + 1
= x² - 2*5*x + 25 + 1
= x² - 10x + 26
To learn more about a function from the given link
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with its given value: