Graph f(x)=-2x^2

Problem

ƒ(x)=−2*x2

Solution

1. Identify the function type, which is a quadratic function in the form ƒ(x)=a*x2

2. Determine the vertex by observing that there are no horizontal or vertical shifts, so the vertex is at (0,0)

3. Determine the direction of opening by looking at the leading coefficient a=−2 Since a<0 the parabola opens downward.

4. Find additional points by substituting x values into the function.

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

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

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

8. Plot the points (0,0) (1,−2) (−1,−2) (2,−8) and (−2,−8) and connect them with a smooth, downward-opening curve.

Final Answer

ƒ(x)=−2*x2

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