Finding the Minimum Value of a Quadratic Function

Very Hard Algebra Functions And Patterns

Consider the function defined by the equation $$f(x) = 2x^2 - 4x + 1$$. Determine the value of $$x$$ for which the function has its minimum value. Subsequently, calculate the minimum value of the function.

To find the vertex of the parabola represented by the quadratic function, apply the formula for the x-coordinate of the vertex, given by $$x = -\f\frac{b}{2a}$$, where $$f(x) = ax^2 + bx + c$$.

Minimum value occurs at $$x = 1$$, with a minimum value of $$f(1) = -1$$.

Minimum value occurs at $$x = 2$$, with a minimum value of $$f(2) = -1$$.

Minimum value occurs at $$x = 2$$, with a minimum value of $$f(2) = 0$$.

Minimum value occurs at $$x = 1$$, with a minimum value of $$f(1) = 0$$.

Minimum value occurs at $$x = 0$$, with a minimum value of $$f(0) = 1$$.

Hint

Submitted12.7K

Correct11.0K

% Correct87%