To find the axis of the graph of the quadratic function f(x) = 4x² + 8x – 7, we need to determine the x-coordinate of the vertex of the parabola defined by this function. The axis of symmetry can be found using the formula:
x = -b / (2a)
In the given function, we identify the coefficients as follows: a = 4 (the coefficient of x²), b = 8 (the coefficient of x), and c = -7 (the constant term). We can now substitute these values into the formula:
x = -8 / (2 * 4)
Calculating this gives:
x = -8 / 8 = -1
Thus, the axis of symmetry for the graph of the function f(x) = 4x² + 8x – 7 is the vertical line x = -1. This means that the graph is symmetric about this line, and the vertex of the parabola, located at this x-coordinate, represents the highest or lowest point on the graph, depending on the direction it opens.