Graph y=4-x^2

Problem

y=4−x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2+b*x+c where a=−1 b=0 and c=4 The graph is a parabola opening downward because a<0

2. Find the y-intercept by setting x=0

y=4−(0)2

y=4

The y-intercept is at (0,4) which is also the vertex since b=0

3. Find the x-intercepts by setting y=0

0=4−x2

x2=4

x=±2

The x-intercepts are at (2,0) and (−2,0)

4. Determine additional points to refine the shape. For x=1

y=4−(1)2

y=3

For x=−1

y=4−(−1)2

y=3

The points (1,3) and (−1,3) are on the graph.

5. Sketch the curve. Plot the vertex (0,4) the x-intercepts (±2,0) and the additional points (±1,3) then connect them with a smooth, downward-opening curve.

Final Answer

y=4−x2

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