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Find the formula for the quadratic equation for a function whose y-intercept is 6 and x intercepts are 45 and 46?

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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.

User Ranzit
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