Determine a Quadratic Function's Minimum or Maximum Value
Determine whether the given quadratic function has a minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
-$$f ( x ) = 4 x ^ { 2 } - 8 x$$
A) minimum; $( 1 , - 4 )$
B) maximum; $( 1 , - 4 )$
C) minimum; $( - 1 , - 4 )$
D) maximum; $( - 1 , - 4 )$

Question

Quizplus · Accepted Answer

The quadratic function $f(x) = 4x^2 - 8x$ has a positive coefficient for $x^2$, indicating it opens upwards and thus has a minimum value. The vertex, or the point of minimum, can be found using $-\frac{b}{2a}$ for $x$, which gives $x = 1$. Substituting $x = 1$ into the function gives $f(1) = 4(1)^2 - 8(1) = -4$, so the minimum point is $(1, -4)$.

Determine a Quadratic Function's Minimum or Maximum Value Determine Whether f(x)=4x2−8xf ( x ) = 4 x ^ { 2 } - 8 xf(x)=4x2−8x

Determine a Quadratic Function's Minimum or Maximum Value
Determine Whether $f ( x ) = 4 x ^ { 2 } - 8 x$