Final answer:
The equation of the parabola with given x-intercepts and y-intercept can be found by setting up the factors that correspond to the x-intercepts, expanding them, and then solving for the coefficient 'a' that will provide the correct y-intercept.
Step-by-step explanation:
To write the equation for a parabola that has its x-intercepts at (1√5, 0) and (-2.8, 0), and its y-intercept at (0, 37.8), we will use the standard form of a parabolic equation, which is y = ax2 + bx + c.
Since we know the x-intercepts, we can determine factors of the parabola to be (x - 1√5) and (x + 2.8). Expanding this we get:
(x - 1√5)(x + 2.8) = x2 + x(2.8 - 1√5) - 2.8(1√5)
Now we need to find the coefficient a that will give us the correct y-intercept (0, 37.8). This can be done by substituting x = 0 into the expanded equation:
a(02 + 0(2.8 - 1√5) - 2.8(1√5)) = 37.8
Solving for 'a' we get a such that:
a = 37.8 / (-2.8(1√5))
Once a is found, replace it back into the expanded equation to get the final equation of the parabola.