Graph y=x^2-5

Problem

y=x2−5

Solution

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

2. Determine the vertex of the parabola by observing that a=1 and k=−5 which places the vertex at (0,−5)

3. Find the y-intercept by setting x=0 resulting in y=−5

4. Calculate the x-intercepts by setting y=0 and solving x2−5=0 which gives x=±√(,5)≈±2.24

5. Select additional points to determine the shape, such as x=1⇒y=−4 and x=2⇒y=−1

6. Plot the points and draw a smooth, upward-opening U-shaped curve (parabola) symmetric about the y-axis.

Final Answer

y=x2−5

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