Graph y=16-x^2

Problem

y=16−x2

Solution

1. Identify the type of function. The equation y=16−x2 is a quadratic function in the form y=a*x2+b*x+c which represents a parabola.

2. Determine the orientation. Since the coefficient of x2 is a=−1 the parabola opens downward.

3. Find the y-intercept. Set x=0 to find the point where the graph crosses the y-axis.

y=16−(0)2

y=16

The y-intercept is (0,16)

4. Find the x-intercepts. Set y=0 and solve for x

0=16−x2

x2=16

x=±4

The x-intercepts are (4,0) and (−4,0)

5. Identify the vertex. For a parabola in the form y=a*x2+c the vertex is located at (0,c)

Vertex=(0,16)

6. Sketch the graph. Plot the vertex (0,16) the x-intercepts (−4,0) and (4,0) and draw a smooth curve opening downward through these points.

Final Answer

y=16−x2

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