Question

What are the coordinates of the vertex for the function f(x) = –16x^2 + 22x + 3 and is it going to be a maximum or minimum?

Answer 1

`\bf \textit{vertex of a parabola}\\ \quad \\ \begin{array}{lccclll} f(x)=&-16x^2&+22x&+3\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)`

if the leading term's coefficient is negative, is going down, if positive, is going up

this one is -16, thus the parabola opens downwards, meaning, goes up up up, reaches a U-turn, the vertex, then goes down down down

so, it reaches a "maximum" point at the vertex