Find the extreme values of the function and where they occur.
-$$y = x ^ { 2 } + 2 x - 3$$
A) The minimum is 1 at $x = - 4$.
B) The minimum is 1 at $x = 4$.
C) The minimum is $- 1$ at $x = 4$.
D) The minimum is $- 4$ at $x = - 1$.

Question

Quizplus · Accepted Answer

The function $y = x^2 + 2x - 3$ is a parabola opening upwards (since the coefficient of $x^2$ is positive). To find the vertex (which gives the extreme value), we use the formula $x = -\frac{b}{2a}$, where $a = 1$ and $b = 2$. Thus, $x = -\frac{2}{2(1)} = -1$. Substituting $x = -1$ into the original equation gives $y = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4$. Therefore, the minimum value is $-4$ at $x = -1$.

Find the Extreme Values of the Function and Where They y=x2+2x−3y = x ^ { 2 } + 2 x - 3y=x2+2x−3

Find the Extreme Values of the Function and Where They $y = x ^ { 2 } + 2 x - 3$