Question

graph the function with a graphing calculator using a standard viewing window. state whether the graph has a turning point in this window.
y = x² - 6
...
choose the correct graph below.
○ a. ○ b. ○ c. ○ d.

Explanation:

Step1: Identify function type

The function $y=x^2-6$ is a quadratic function, which has a parabola graph opening upward (since the coefficient of $x^2$ is positive).

Step2: Find vertex (turning point)

For $y=ax^2+bx+c$, vertex x-coordinate is $x=-\frac{b}{2a}$. Here $a=1$, $b=0$, so $x=0$. Substitute $x=0$: $y=0^2-6=-6$. The vertex is $(0,-6)$, which is a minimum (turning point).

Step3: Match to options

Option A shows an upward-opening parabola with vertex below the x-axis, matching $y=x^2-6$. Options B/C/D are downward-opening or have incorrect vertex positions.

Step4: Check turning point in window

The standard viewing window (typically $x: [-10,10], y: [-10,10]$) includes the vertex $(0,-6)$, so there is a turning point in the window.

Answer:

A. [The upward-opening parabola graph with vertex below the x-axis]
The graph has a turning point in the standard viewing window.