Question

1. is the vertex at a maximum or a minimum? how do you know?

y = 2x^2 + 20x - 2

Explanation:

Step1: Identify the form of quadratic function

The general form of a quadratic function is $y = ax^{2}+bx + c$, and in the given function $y = 2x^{2}+20x - 2$, we have $a = 2$, $b=20$, $c=-2$.

Step2: Use the sign of the leading - coefficient

For a quadratic function $y = ax^{2}+bx + c$, if $a>0$, the parabola opens upward; if $a < 0$, the parabola opens downward. Since $a = 2>0$ in the function $y = 2x^{2}+20x - 2$, the parabola opens upward.

Step3: Determine the nature of the vertex

The vertex of a parabola is either a maximum or a minimum. When the parabola opens upward, the vertex is a minimum point.

Answer:

The vertex is a minimum because the coefficient of $x^{2}$ ($a = 2$) is positive, so the parabola opens upward.