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.
-$$f ( x ) = x ^ { 2 } + 2 x - 3$$
A) minimum; $( - 1 , - 4 )$
B) maximum; $( - 1 , - 4 )$
C) minimum; $( - 4 , - 1 )$
D) maximum; $( - 4 , - 1 )$

Question

Quizplus · Accepted Answer

The quadratic function $f(x) = x^2 + 2x - 3$ is in the form $ax^2 + bx + c$, where $a = 1$, $b = 2$, and $c = -3$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex (minimum point) can be found using the formula $-\frac{b}{2a}$ for the x-coordinate, which gives $-\frac{2}{2(1)} = -1$. Plugging this back into the function gives the y-coordinate: $(-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4$. Therefore, the minimum point is $(-1, -4)$.

Determine a Quadratic Function's Minimum or Maximum Value Determine Whether f(x)=x2+2x−3f ( x ) = x ^ { 2 } + 2 x - 3f(x)=x2+2x−3

Determine a Quadratic Function's Minimum or Maximum Value
Determine Whether $f ( x ) = x ^ { 2 } + 2 x - 3$