Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = x ^ { 2 } + 4 x - 3$$
A) maximum at $( - 7 , - 2 )$
B) minimum at $( - 2 , - 7 )$
C) maximum at $( 0 , - 2 )$
D) minimum at $( - 7,0 )$

Question

Quizplus · Accepted Answer

The quadratic function is in the form $f(x) = ax^2 + bx + c$, where $a = 1$, $b = 4$, and $c = -3$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex of the parabola, which gives the minimum value, can be found using the formula $(-b/2a, f(-b/2a))$. Substituting $a = 1$ and $b = 4$ gives the vertex as $(-2, -7)$, which is the minimum point.

Use the Quadratic Function to Determine If the Function Has f(x)=x2+4x−3f ( x ) = x ^ { 2 } + 4 x - 3f(x)=x2+4x−3

Use the Quadratic Function to Determine If the Function Has $f ( x ) = x ^ { 2 } + 4 x - 3$