Graph y=-5x^2

Problem

y=−5*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 and width. Because the coefficient a=−5 is negative, the parabola opens downward. Since |−5|>1 the parabola is narrower than the parent function y=x2

4. Calculate additional points to plot. Choose xvalues around the vertex to find corresponding yvalues.

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

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

7. Substitute x=2 y=−5*(2)2=−20 This gives the point (2,−20)

8. Sketch the curve. Plot the points (0,0) (1,−5) (−1,−5) (2,−20) and (−2,−20) then connect them with a smooth, downward-opening curve.

Final Answer

y=−5*x2

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