Question

question 13.
the table represents some points on the graph of quadratic function $g$.
what is the range of $g$
a. all real numbers less than or equal to $\frac{3}{2}$
b. all real numbers less than or equal to $\frac{19}{4}$

Explanation:

Step1: Identify vertex of quadratic

The quadratic function's graph is symmetric. Looking at the table, $g(1)=4$, $g(2)=4$, $g(\frac{1}{2})=g(\frac{5}{2})=\frac{7}{4}$. The vertex (maximum point, since values decrease after $\frac{3}{2}$) is at $x=\frac{3}{2}$, where $g(\frac{3}{2})=\frac{19}{4}$.

Step2: Determine the range

Quadratic opens downward (since values decrease from the vertex), so the maximum value is $\frac{19}{4}$, and the function takes all values less than or equal to this maximum.

Answer:

B. All real numbers less than or equal to $\frac{19}{4}$