Answer :
The quadratic function satisfying the given conditions is f(x) = 2x² - 5x - 7.
To find the quadratic function f(x)= ax²+bx+c with the given values f(1)=-10, f(-3)=46, and f(3)=-2, we can set up a system of equations:
a[tex](1)^2[/tex] + b(1) + c = -10
a[tex](-3)^2[/tex] + b(-3) + c = 46
a[tex](3)^2[/tex] + b(3) + c = -2
By substituting and simplifying, these become:
a + b + c = -10
9a - 3b + c = 46
9a + 3b + c = -2
Through a process of elimination and substitution, we determine that:
a = 2
b = -5
c = -7
Therefore, the quadratic function is f(x) = 2x² - 5x - 7.