Answer:
x=-6
Step-by-step explanation:
<span>The center, vertex, and focus all lie on the line y = 0. Then we know that the equation of a hyperbola is a^2 + b^2 = c^2 . a^2 represents the x part of the equation and the y part will be subtracted. We know that the vertex is 48 units from the center and that the focus is 50 units from the center. Then we have that b^2 = 2500 - 2304 = 196 .
Thus the equation that represents the hyperbola is x^2/2304 - y^2/196 = 1 or 49x^2 -576y^2 - 112896 = 0</span>
To find the minimum, take the derivative of the function and equate to zero:
f(x) = y = x² + ax + b
dy/dx = 2x + a = 0
Substitute x =6:
a = -2x
a = -2(6)
a = -12
Then, substitute x = 6, y = 7 and a = -12 to find b.
7 = (6)² -12(6) + b
7 + 36 = b
b = 43
Thus, a = -12 and b = 43
