Determine whether the given quadratic function has a minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
-$$f ( x ) = 2 x ^ { 2 } - 4 x$$
A) minimum; $( 1 , - 2 )$
B) maximum; $( 1 , - 2 )$
C) minimum; $( - 1 , - 2 )$
D) maximum; $( - 1 , - 2 )$

Question

Quizplus · Accepted Answer

The coefficient of $x^2$ is positive (2), indicating the parabola opens upwards, hence it has a minimum. The vertex (minimum point) can be found using $-\frac{b}{2a}$ for $x$, which gives $1$, and substituting $x = 1$ into the function gives $-2$ for $y$, resulting in the point $(1, -2)$.

Determine Whether the Given Quadratic Function Has a Minimum Value f(x)=2x2−4xf ( x ) = 2 x ^ { 2 } - 4 xf(x)=2x2−4x

Determine Whether the Given Quadratic Function Has a Minimum Value $f ( x ) = 2 x ^ { 2 } - 4 x$