To solve this problem, we first need to find the x-intercepts of the quadratic equation \( y = -4x^2 + 12x + 40 \). The x-intercepts occur where \( y = 0 \). Therefore, we set the quadratic equation to zero and solve for \( x \):
[tex]\[ -4x^2 + 12x + 40 = 0 \][/tex]
Using a method such as factoring, completing the square, or the quadratic formula, we find the roots of the equation. Since we already have the roots given as \( -2 \) and \( 5 \), the x-intercepts are at the points where the value of \( y \) is zero, i.e., at \( (x, 0) \).
Thus, the x-intercepts are at:
[tex]\[ (-2, 0) \][/tex]
and
[tex]\[ (5, 0) \][/tex]
Now, we match these points with the provided choices:
a. \((2, 0); (-5, 0)\)
b. \((-2, 0); (-5, 0)\)
c. \((-2, 0); (5,0)\)
d. \((2, 0); (5, 0)\)
The correct choice is:
c. \((-2, 0); (5, 0)\)
Therefore, the best answer from the choices provided is:
C
