Question

compare f(x) = -0.3x² - 0.6x + 0.6 to function g, shown in the graph. what are the maximum values? which function has the greater maximum value? the maximum value of f is \\(\square\\), and the maximum value of g is \\(\square\\), so \\(\square\\) has the greater maximum value. (type integers or decimals rounded to the nearest tenth as needed.)

Explanation:

Step1: Find vertex x of f(x)

For quadratic $ax^2+bx+c$, $x=-\frac{b}{2a}$.
Here $a=-0.3, b=-0.6$, so $x=-\frac{-0.6}{2(-0.3)} = -1$

Step2: Calculate max f(x)

Substitute $x=-1$ into $f(x)$:
$f(-1)=-0.3(-1)^2 -0.6(-1)+0.6 = -0.3 + 0.6 + 0.6 = 0.9$

Step3: Identify max g(x) from graph

The vertex of $g(x)$ (the highest point) has a y-value of 4.

Answer:

The maximum value of f is 0.9, and the maximum value of g is 4, so g has the greater maximum value.