Graph -3x^2

Problem

y=−3*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 where a=−3

2. Determine the shape and orientation. Since a is negative, the graph is a parabola that opens downward.

3. Locate the vertex. For the basic form y=a*x2 the vertex is at the origin (0,0)

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

5. Calculate for x=1 y=−3*(1)2=−3 This gives the point (1,−3)

6. Calculate for x=−1 y=−3*(−1)2=−3 This gives the point (−1,−3)

7. Calculate for x=2 y=−3*(2)2=−12 This gives the point (2,−12)

8. Plot the points (0,0) (1,−3) (−1,−3) (2,−12) and (−2,−12) and connect them with a smooth curve.

Final Answer

y=−3*x2

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