something noteworthy is that the squared variable is the "x", thus the parabola is a vertical one, the "p" value is negative, so is opening downwards, and the h,k is pretty much the origin,
vertex is at (0,0)
the focus point is "p" or 5 units down from there, namely at (0, -5)
the directrix is "p" units on the opposite direction, up, namely at y = 5
the focal width, well, |4p| is pretty much the focal width, in this case, is simply yeap, you guessed it, 20.
<u>Answer-</u>
<em>The statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.</em>
<u>Solution-</u>
It solely depends on b, whether the function will have one or two or zero x intercept.
This plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e V shape, with vertex translated to (-a, b), instead of origin.
1- If b is zero, the graph will have exactly one x-intercept, at x= -a
2- If b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.
3- If b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.
∴ The statement is sometimes true.
