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.