Graphing a parabola of the form \( y=a x^{2} \) 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 rig a-function button. \( \qquad \)

To graph the parabola \( y = -x^2 \), start by identifying the vertex, which for this equation is at the point \( (0, 0) \). Since the coefficient \( a \) is negative, the parabola opens downwards. Now, let's plot some points. For \( x = -2 \): \[ y = -(-2)^2 = -4 \quad \text{(Point: } (-2, -4) \text{)} \] For \( x = -1 \): \[ y = -(-1)^2 = -1 \quad \text{(Point: } (-1, -1) \text{)} \] For \( x = 0 \): \[ y = 0 \quad \text{(Vertex: } (0, 0) \text{)} \] For \( x = 1 \): \[ y = -(1)^2 = -1 \quad \text{(Point: } (1, -1) \text{)} \] For \( x = 2 \): \[ y = -(2)^2 = -4 \quad \text{(Point: } (2, -4) \text{)} \] Now you have the points: \( (-2, -4) \), \( (-1, -1) \), \( (0, 0) \), \( (1, -1) \), and \( (2, -4) \). Plot these points on a graph, connect them with a smooth curve, and you will see the classic downward-opening parabola! Fun fact: Parabolas are everywhere in nature, from the trajectory of a ball to the shape of satellites! If you ever accidentally plot your points incorrectly or misconnect them, don’t fret! Start by verifying each point by substituting back into the equation. Keeping your calculations organized can help avoid common mistakes. Happy graphing!