Answer:
To write the quadratic function in standard form, we first need to determine its intercept form.
If a quadratic function passes through the points (-9, 0), (2, 0), and (1, 10), then its intercept form can be written as:
f(x) = A(x + 9)(x - 2)
where A is a constant that we need to determine.
To find the value of A, we can substitute the coordinates of the third point into the equation:
10 = A(1 + 9)(1 - 2)
10 = -10A
Dividing by -10 on both sides, we get:
A = -1
Substituting this value of A back into the intercept form, we get:
f(x) = -(x + 9)(x - 2)
Expanding this equation, we get:
f(x) = -x^2 - 7x - 18
This is now in standard form, which is:
f(x) = ax^2 + bx + c
where a = -1, b = -7, and c = -18.