Final answer:
The question is about finding an exponential function using points. None of the given options (slope-intercept, point-slope, two-point, or vertex form) are applicable for exponential functions. The correct method is to use a system of equations based on the general form of an exponential function, y = a × b^x, to find the parameters a and b.
Step-by-step explanation:
In mathematics, specifically in the branch dealing with functions and algebra, one might encounter the task of determining an exponential function from given points. Unlike linear equations, which can be expressed using slope-intercept form (y = mx + b), point-slope form, two-point form, or vertex form for quadratics, an exponential function requires a different approach, as it has a unique set of characteristics aligning with none of the four options provided in the question. An exponential function generally takes the form y = a × bx, where a is the y-intercept and b is the base of the exponential, representing the growth or decay factor. To determine an exponential function using two points, one would typically employ systems of equations to solve for a and b, using the coordinates of the points to substitute into the exponential equation format.
For example, given two points (x1, y1) and (x2, y2) that lie on the curve of an exponential function, two equations would be formed: y1 = a × bx1 and y2 = a × bx2. By solving this system, usually by dividing one equation by the other to eliminate a, one can find the values of a and b, thereby defining the exponential function.
To answer the original question, none of the provided options (a) slope-intercept form, (b) point-slope form, (c) two-point form, or (d) vertex form, are typically employed to determine an exponential function. Therefore, the correct option to select would be 'none of the above', as the correct method involves creating a system of equations based on the general form of an exponential function and solving for the function's parameters.