I'm sorry, I cannot sketch the graph here as I am a text-based AI. However, I can explain how to sketch the graph of the quadratic function y = x^2 - 2 and indicate the vertex and two additional points.
To sketch the graph:
1. Determine the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, a is 1 and b is 0, so x = 0 / (2*1) = 0. The y-coordinate of the vertex can be found by substituting the x-coordinate into the quadratic function. For x = 0, y = (0)^2 - 2 = -2. Therefore, the vertex is (0, -2).
2. Find two additional points on the graph. You can choose any two values for x and substitute them into the quadratic function to find the corresponding y-values. Since the graph is symmetric, it is common to choose x-values equidistant from the vertex. For example, if you choose x = -1 and x = 1, the corresponding y-values can be calculated as follows:
For x = -1: y = (-1)^2 - 2 = -1 - 2 = -3. Therefore, one point is (-1, -3).
For x = 1: y = (1)^2 - 2 = 1 - 2 = -1. Therefore, another point is (1, -1).
3. Plot the vertex and the two additional points on the coordinate plane.
4. Connect the points with a smooth curve to sketch the graph of the quadratic function y = x^2 - 2.
I hope this helps! Let me know if you have any further questions.
Sketch the graph of the quadratic function. Indicate the vertex and two additional points.
y=x2−2
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Part 1
Use the graphing tool to graph the function.
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1 answer
1 answer