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Write an equation of a parabola with x-intercepts at (3, 0) and (-3,0) and which passes through the point (1, 2).​

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Final answer:

The equation of the parabola with x-intercepts at (3, 0) and (-3, 0) and passing through (1, 2) is y = -1/4(x - 3)(x + 3), which expands to y = -1/4x^2 + 9/4.

Step-by-step explanation:

To write an equation of a parabola with x-intercepts at (3, 0) and (-3, 0) and which passes through the point (1, 2), we start by using the factored form of the parabola's equation:

y = a(x - x1)(x - x2)

where x1 and x2 are the roots, so in this case:

y = a(x - 3)(x + 3)

Now, we need to use the point (1, 2) that lies on the parabola to find the value of 'a'. We substitute the point into the equation and solve for 'a':

2 = a(1 - 3)(1 + 3)

2 = a(-2)(4)

2 = -8a

a = -2 / 8

a = -1 / 4

So, the equation of the parabola is:

y = -1/4(x - 3)(x + 3)

To expand this and write it in standard form:

y = -1/4(x^2 - 9)

y = -1/4x^2 + 9/4

This is the desired equation of the parabola.

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