charla wants to determine the vertex of the function f(x) = x² - 18x + 60 by changing the function into…

Explanation:

Step1: Convert to vertex - form

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. For the function $f(x)=x^{2}-18x + 60$, we complete the square. [ \begin{align*} f(x)&=x^{2}-18x+60\ &=(x^{2}-18x)+60\ &=(x^{2}-18x + 81-81)+60\ &=(x - 9)^{2}-81 + 60\ &=(x - 9)^{2}-21 \end{align*} ] The vertex of the function is $(9,-21)$.

Step2: Analyze each option

• Option 1: The $x$-coordinate of the vertex is $9$ and the $y$-coordinate is $-21$. Since $9>-21$, the $x$-coordinate of the vertex is greater than the $y$-coordinate.
• Option 2: The $x$-coordinate of the vertex $h = 9$ is positive, not negative.
• Option 3: The $y$-intercept is found by setting $x = 0$. So $f(0)=0^{2}-18\times0 + 60=60$. The $y$-coordinate of the vertex is $-21$, and $-21<60$.
• Option 4: The $y$-coordinate of the vertex is $-21$, which is negative.

Answer:

The x - coordinate of the vertex is greater than the y - coordinate.