Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = 4 x ^ { 2 } + 8 x$$
A) minimum at $( - 1 , - 4 )$
B) maximum at $( 1 , - 4 )$
C) minimum; (ii) $( 1 , - 4 )$
D) maximum at $( - 1 , - 4 )$

Question

Quizplus · Accepted Answer

The coefficient of $x^2$ is positive (4), indicating the parabola opens upwards and hence has a minimum value. To find the vertex (which gives the minimum value), use the formula $-\frac{b}{2a}$ for the x-coordinate: $-\frac{8}{2*4} = -1$. Plugging this back into the function gives $f(-1) = 4(-1)^2 + 8(-1) = 4 - 8 = -4$. So, the minimum is at $(-1, -4)$.

Use the Quadratic Function to Determine If the Function Has f(x)=4x2+8xf ( x ) = 4 x ^ { 2 } + 8 xf(x)=4x2+8x

Use the Quadratic Function to Determine If the Function Has $f ( x ) = 4 x ^ { 2 } + 8 x$