Question

graph the parabola.
( y = -x^2 )
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

For the parabola \( y = -x^2 \), the vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h,k)\) is the vertex. Here, \( h = 0 \), \( k = 0 \), so the vertex is \((0,0)\).

Step2: Find points left of vertex (x negative)

Let \( x = -1 \): \( y = -(-1)^2 = -1 \), so point \((-1, -1)\).
Let \( x = -2 \): \( y = -(-2)^2 = -4 \), so point \((-2, -4)\).

Step3: Find points right of vertex (x positive)

Let \( x = 1 \): \( y = -(1)^2 = -1 \), so point \((1, -1)\).
Let \( x = 2 \): \( y = -(2)^2 = -4 \), so point \((2, -4)\).

Answer:

Vertex: \((0, 0)\), Left points: \((-1, -1)\), \((-2, -4)\), Right points: \((1, -1)\), \((2, -4)\) (These points can be plotted to graph the parabola \( y = -x^2 \))