Question

compare ( g(x) = -1.5x^2 - 4.5x + 10 ) to ( f ), shown in the graph. which function has a greater maximum value?

choose the correct answer below.

a. ( g(x) ). the ( y )-coordinate of the vertex of ( g(x) ) is greater than the ( y )-coordinate of the vertex of ( f(x) ).

b. ( g(x) ). the ( x )-coordinate of the vertex of ( g(x) ) is greater than the ( x )-coordinate of the vertex of ( f(x) ).

c. ( f(x) ). the ( y )-coordinate of the vertex of ( f(x) ) is greater than the ( y )-coordinate of the vertex of ( g(x) ).

Explanation:

Step1: Find vertex x of g(x)

For quadratic $ax^2+bx+c$, $x=-\frac{b}{2a}$
$x=-\frac{-4.5}{2(-1.5)} = -1.5$

Step2: Calculate g(x) vertex y-value

Substitute $x=-1.5$ into $g(x)$:
$g(-1.5)=-1.5(-1.5)^2 -4.5(-1.5)+10$
$g(-1.5)=-1.5(2.25)+6.75+10$
$g(-1.5)=-3.375+6.75+10=13.375$

Step3: Identify f(x) vertex y-value

From graph, vertex of f(x) is at $y=16$

Step4: Compare maximum values

$16 > 13.375$, so f(x) has greater maximum.

Answer:

C. f(x); The y-coordinate of the vertex of f(x) is greater than the y-coordinate of the vertex of g(x).