Graph -2x^2

Problem

y=−2*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 which represents a parabola.

2. Determine the vertex. Since there are no horizontal or vertical shifts, the vertex is at the origin (0,0)

3. Analyze the direction of opening. Because the coefficient a=−2 is negative, the parabola opens downward.

4. Find additional points to determine the width. Substitute simple x values into the equation to find corresponding y values.

5. Calculate for x=1 y=−2*(1)2=−2 This gives the point (1,−2)

6. Calculate for x=2 y=−2*(2)2=−8 This gives the point (2,−8)

7. Use symmetry across the y-axis (x=0 to find the corresponding points (−1,−2) and (−2,−8)

8. Plot the vertex (0,0) and the calculated points, then draw a smooth curve connecting them to form the downward-opening parabola.

Final Answer

y=−2*x2

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