Question

For what value of x will the function f(x)=1−2x ²have the minimum value?

A) x=0
B) x=1
C) x=−1
D) There is no minimum value.

Answer 1

The minimum value of the quadratic function f(x)=1−2x² occurs at x=0, corresponding to option A, which can be determined by using the vertex formula for quadratics.

Step-by-step explanation:

For what value of x will the function f(x)=1−2x² have the minimum value? To determine the minimum value of a quadratic function in the form of f(x) = ax² + bx + c, where a, b, and c are constants and the coefficient a is negative, indicating the parabola opens downwards, we can use the vertex formula x = -b/(2a) to find the x-coordinate of the vertex, which corresponds to the minimum point for downward opening parabolas. In this specific function, a = -2 and b = 0. Applying the formula, we get x = -0/(2*(-2)) = 0. Therefore, the minimum value of the function occurs at x=0, which corresponds to option A).