Question

graph the parabola.
$y = x^2 - 6$
plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph-a-function button.

Explanation:

Step1: Find the vertex

The parabola is in the form \( y = x^2 + k \), so the vertex is at \( (0, -6) \) (since for \( y = x^2 - 6 \), \( h = 0 \), \( k=-6 \)).

Step2: Find points left of vertex (x negative)

• For \( x = -1 \): \( y = (-1)^2 - 6 = 1 - 6 = -5 \), so point \( (-1, -5) \).
• For \( x = -2 \): \( y = (-2)^2 - 6 = 4 - 6 = -2 \), so point \( (-2, -2) \).

Step3: Find points right of vertex (x positive)

• For \( x = 1 \): \( y = (1)^2 - 6 = 1 - 6 = -5 \), so point \( (1, -5) \).
• For \( x = 2 \): \( y = (2)^2 - 6 = 4 - 6 = -2 \), so point \( (2, -2) \).

Answer:

Vertex: \((0, -6)\), Left points: \((-1, -5)\), \((-2, -2)\), Right points: \((1, -5)\), \((2, -2)\) (plot these points and draw the parabola).