Question

The quadratic functions f(x) and g(x) are described as follows: f(x) = −4x2 + 5
x g(x)
0 0
1 1
2 5
3 1
4 0
Which of the following statements best compares the maximum value of the 2 functions?

Answer 1

well, what's the maximum value for g(x) anyway? look at the table

Answer 2

5?

Answer 3

well.. yes is 5
now let's take a peek at the vertex of f(x)
the vertex is the U-turn of the graph, and thus is where it'll changes directions

so for \(\bf f(x) = −4x^2 + 5\) that'll be at \(\bf \textit{vertex of a parabola}\\ \quad \\
f(x)=-4x^2+5\iff y = {\color{red}{ -4}}x^2{\color{blue}{ +0}}x{\color{green}{ +5}}\qquad

\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

so.. see what you get for "y" there, and that's the highest point of it, because is its vertex
since the leading term coefficient is negative, -4, that means the parabola is going downwards, thus the vertex is the highest point, it goes UP then makes the U-turn and back down

Answer 5

so g(x) has the greater maximum value?

Answer 6

hmmm ever found the vertex for f(x)?