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the parabola y=2x^2 is translated to a new parabola with x intercepts 4 and -3.
The y-intercept of the new parabola is
a.12
b.-12
c.-0.5
d.-24
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Translations of a parabola do not change the coefficient at x^2.
From the other side, the symmetry line of the new parabola is x = = 0.5
Therefore, the new parabola is y = 2*(x-0.5)^2 + b, where b is an unknown value.
To find "b", use the condition that x-intercept is 4:
y = 0 = 2*(x-0.5)^2 + b at x= 4,
or
0 = 2*(4-0.5)^2 + b,
0 = 2*3.5^2 + b
0 = 24.5 + b
b = - 24.5.
Thus the new parabola is y = 2*(x-0.5)^2 - 24.5, and its value at x= 0 is
y = 2*(0-0.5)^2 - 24.5 = 2*0.5^2 - 24.5 = -24. ANSWER
Solved.
Another, even more simple and short straightforward solution is possible.
Since the new parabola has x-intercepts 4 and -3, the new quadratic function has the form
y = a*(x+3)*(x-4)
With some real coefficient "a".
Since translations leave the leading coefficient at x^2 unchangeable, a = 2.
It implies that the new quadratic function is y = 2*(x+3)*(x-4).
Therefore, y-intercept of the new parabola is y(0) = 2*(0+3)*(0-4) = 2*3*(-4) = -24. ANSWER
Solved (by another way).