Graph y=-4x^2

Problem

y=−4*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 where a=−4

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=−4 is negative, the parabola opens downward.

4. Calculate the vertical stretch. The absolute value |−4|=4 indicates that the parabola is narrower than the parent function y=x2 by a factor of 4.

5. Find additional points to plot. Choose xvalues around the vertex:

   • If x=1 y=−4*(1)2=−4 Point: (1,−4)

   • If x=−1 y=−4*(−1)2=−4 Point: (−1,−4)

   • If x=2 y=−4*(2)2=−16 Point: (2,−16)

6. Sketch the curve. Plot the points (0,0) (1,−4) and (−1,−4) then draw a smooth downward-opening curve through them.

Final Answer

y=−4*x2

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