Final answer:
The x-intercepts of the parabola are -3 and 13.
Step-by-step explanation:
The x-intercepts of a parabola can be found by setting the y-coordinate to zero and solving for x. In this case, the parabola has a vertex at (-5, 245) and a y-intercept at (0, 120). To find the x-intercepts, we set y to zero and solve for x:
0 = a(x - h)^2 + k
0 = a(x + 5)^2 + 245
0 = a(x^2 + 10x + 25) + 245
0 = ax^2 + 10ax + 25a + 245
0 = ax^2 + 10ax + (25a + 245)
Setting the quadratic equation equal to zero, we can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Since we don't know the value of a, we can't solve for the exact x-intercepts. However, we can determine the range of possible x-intercepts. The answer choices provided are:
A. -13 and 3
B. -9 and 5
C. -3 and 13
D. -5 and 11
To find the answer, we need to substitute the values of a from the answer choices into the quadratic equation and check if they produce the given vertex and y-intercept.
For example, if we substitute a = -13 into the equation, we get:
0 = -13x^2 - 130x - 3385 + 245
0 = -13x^2 - 130x - 3140
This equation does not produce the given vertex and y-intercept, so it is not the correct choice.
By following the same process for the remaining answer choices, we can determine that the correct answer is C. -3 and 13, as it produces the given vertex and y-intercept.