below:
y = x^(2) + 4x - 45
To change this equation into the form y = (x - h)^(2) + k, we need to complete the square.
First, let's group the terms involving x:
y = (x^(2) + 4x) - 45
Next, we need to find the value of h. To do this, we take half of the coefficient of x (which is 4) and square it:
h = (4/2)^(2) = 2^(2) = 4
Now, we can rewrite the equation as:
y = (x^(2) + 4x + 4) - 45 + 4
Simplifying further:
y = (x + 2)^(2) - 41
Finally, we have successfully changed the equation into the form y = (x - h)^(2) + k, where h = 2 and k = -41.