To find the axis of the graph of the function f(x) = 4x² + 8x – 7, we need to identify the vertex of the parabola, as this point will lie on the axis of symmetry. The standard form of a quadratic equation is:
f(x) = ax² + bx + c
In our case, the coefficients are:
- a = 4
- b = 8
- c = -7
The x-coordinate of the vertex (also the axis of symmetry) can be found using the formula:
x = -b / (2a)
Plugging our values into the formula:
x = -8 / (2 * 4)
This simplifies to:
x = -8 / 8 = -1
Thus, the axis of symmetry for the graph of the function is x = -1.
To summarize, the axis of the graph for the function f(x) = 4x² + 8x – 7 is x = -1. This vertical line divides the parabola into two symmetric halves, allowing you to predict that any point on one side has a corresponding point on the other side at an equal distance from the axis.