Question

What is the maximun or minimum vlaue of the equation? what is the range?
y=2x squared +32x -16

Answer 1

have you covered parabolas yet?

Answer 2

Yes

Answer 3

ok.... .so notice the leading term, is positive, meaning the parabola opens UP
if it opens UP, that means it has a bottom, or a "minimum" point which is at its vertex

to find the vertex of the parabola or a quadratic equation, \(\bf y={\color{red}{ 2}}x^2{\color{blue}{ 32}}x {\color{green}{ -16}}
\\ \quad \\

\textit{vertex of a parabola}\\ \quad \\

\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)\)

Answer 4

hmm missing a sign there =) \(\bf y={\color{red}{ 2}}x^2{\color{blue}{ +32}}x {\color{green}{ -16}}
\\ \quad \\

\textit{vertex of a parabola}\\ \quad \\

\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)\)