Find the value of c that gives the function the given minimum value.
-$$f ( x ) = 5 x ^ { 2 } - 10 x + c ; \text { minimum value } 1$$
A) -5
B) 5
C) c = -4
D) c = 6

Question

Quizplus · Accepted Answer

The minimum value of a quadratic function $ f(x) = ax^2 + bx + c $ occurs at $ x = -\frac{b}{2a} $. For $ f(x) = 5x^2 - 10x + c $, the minimum occurs at $ x = 1 $. Substituting $ x = 1 $ into the function gives $ f(1) = 5(1)^2 - 10(1) + c = 5 - 10 + c = c - 5 $. Setting this equal to the given minimum value 1, we solve $ c - 5 = 1 $ to find $ c = 6 $.

Find the Value of C That Gives the Function the Given