Final answer:
The equation of the quadratic function with x-intercepts at -1 and -10 that passes through the point (-7, -0.9) is f(x) = 0.05(x + 1)(x + 10). To find this, we use the point (-7, -0.9) to determine the 'a' value in the factored form of the quadratic function.
Step-by-step explanation:
The task presented is to determine the equation of a quadratic function that has x-intercepts at -1 and -10 and passes through the point (-7, -0.9). First, we need to understand that a quadratic function is typically represented in the form f(x) = ax2 + bx + c, where the x-intercepts are the values of x for which f(x) = 0. Given the x-intercepts are -1 and -10, we can write the function in its factored form as f(x) = a(x + 1)(x + 10). Since the graph passes through the point (-7, -0.9), we substitute x with -7 and f(x) with -0.9 to find the value of 'a'.
Substituting, we get: -0.9 = a(-7 + 1)(-7 + 10), which simplifies to -0.9 = a(-6)(3), or -0.9 = -18a. Solving for 'a', we find that a = 0.05. Thus, the equation of the quadratic function is: f(x) = 0.05(x + 1)(x + 10).
Understanding the y-intercept is also beneficial, although it is not directly asked in the question. The y-intercept is the point where the graph crosses the y-axis, which occurs when x = 0. However, when considering physical scenarios such as test scores, a y-intercept that involves an x value of 0 may not be meaningful, as such values might not exist or be possible in the context.