Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. If necessary, round answers to two decimal places.
-$$f ( x ) = x ^ { 2 } + 2 x - 3 ; ( - 5,5 )$$
A) local maximum at $( 1 , - 4 )$
B) local maximum at $( - 1,4 )$
C) local minimum at $( - 1 , - 4 )$
D) local minimum at $( 1,4 )$

Question

Quizplus · Accepted Answer

The function $f(x) = x^2 + 2x - 3$ is a parabola opening upwards, so it has a local minimum but no local maximum. The vertex of this parabola, given by $-\frac{b}{2a}$ for a quadratic equation $ax^2 + bx + c$, is at $x = -\frac{2}{2(1)} = -1$. Substituting $x = -1$ into the function gives $f(-1) = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4$, so the local minimum is at $(-1, -4)$.

Use a Graphing Utility to Graph the Function Over the Indicated