Final answer:
The quadratic equation for a function with y-intercept 6 and x-intercepts 45 and 46 is y = (1/345)(x - 45)(x - 46). We found this by using the factored form of a quadratic equation and substituting the given intercepts to solve for the coefficient 'a'.
Step-by-step explanation:
To find the formula for the quadratic equation of a function with a given y-intercept and x-intercepts, we can use the vertex form or the factored form of a quadratic equation. Since we have the x-intercepts and the y-intercept, it's convenient to use the factored form:
y = a(x - x1)(x - x2)
Where x1 and x2 are the x-intercepts and a is a coefficient that will affect the stretching or compression of the parabola. We know the x-intercepts are 45 and 46, so:
y = a(x - 45)(x - 46)
Since the y-intercept is the point where x=0, we substitute x with 0 and y with 6, the given y-intercept, to find the value of a.
6 = a(0 - 45)(0 - 46)
6 = a(-45)(-46)
a = 6 / (45 × 46)
a = 6 / 2070
a = 1 / 345
Now we have the value of a, we can write the quadratic equation:
y = (1/345)(x - 45)(x - 46)
This is the quadratic equation for the function with the given intercepts.