Graph y=x^2-6

Problem

y=x2−6

Solution

1. Identify the type of function, which is a quadratic function in the form y=a*x2+c

2. Determine the vertex of the parabola. Since there is no x term, the xcoordinate of the vertex is 0

3. Calculate the yintercept by substituting x=0 into the equation.

y=0−6

y=−6

4. Find the xintercepts by setting y=0 and solving for x

0=x2−6

x2=6

x=±√(,6)≈±2.45

5. Plot additional points to determine the shape. For x=1 and x=−1

y=(±1)2−6

y=−5

6. Sketch the graph as a parabola opening upward with its vertex at (0,−6)

Final Answer

y=x2−6

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