Graph y=-3/4x^2

Problem

y=−3/4*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 which represents a parabola with its vertex at the origin (0,0)

2. Determine the direction of the opening. Since the coefficient a=−3/4 is negative, the parabola opens downward.

3. Calculate the coordinates of several points to determine the shape. Choose x values that are multiples of 2 to simplify the fraction.

4. Substitute x=0

y=−3/4*(0)2=0

The vertex is (0,0)

5. Substitute x=2 and x=−2

y=−3/4*(2)2=−3/4*(4)=−3

The points are (2,−3) and (−2,−3)

6. Substitute x=4 and x=−4

y=−3/4*(4)2=−3/4*(16)=−12

The points are (4,−12) and (−4,−12)

7. Plot the points (0,0) (2,−3) (−2,−3) (4,−12) and (−4,−12) on a coordinate plane and connect them with a smooth, downward-opening curve.

Final Answer

y=−3/4*x2

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