Based on the calculations using the given x-intercept of this graph, the value of a is equal to 11.
A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
In Mathematics, the y-intercept of any graph (parabola) occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
Given that the x-intercept is at (a, 0), we would simply substitute the given points as follows:
y = (x − 4)^2 − 49
0 = (a − 4)^2 − 49
(a − 4)^2 = 49
Taking the square of both sides, we have:
a - 4 = √49
a - 4 = 7
a = 7 + 4
a = 11.
Read more on x-intercept here: https://brainly.com/question/24363347
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