Question

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = 9 - x2

Accepted Answer

Step 1: Understand the equation. The given equation is y = 9 - $$x^2. $$This is a quadratic equation, and its graph will be a parabola. The term $$-x^2$$ indicates that the parabola opens downward because the coefficient of $$x^2 is $$negative. Step 2: Create a table of values. Substitute the given x-values (-3, -2, -1, 0, 1, 2, 3) into the equation y = 9 - $$x^2 to $$calculate the corresponding y-values. For example, when x = -3, y = 9 - $$(-3)^2 = 9 - 9 = 0. $$Repeat this process for all x-values. Step 3: Plot the points. Once you have the table of values, plot the points (x, y) on a coordinate plane. For example, if x = -3 gives y = 0, plot the point (-3, 0). Repeat for all other x-values. Step 4: Draw the graph. After plotting all the points, connect them smoothly to form the parabola. Ensure the curve is symmetric about the y-axis, as the equation y = 9 - $$x^2 is $$symmetric with respect to the y-axis. Step 5: Analyze the graph. The vertex of the parabola is at (0, 9), which is the maximum point since the parabola opens downward. The x-intercepts are the points where y = 0, and the y-intercept is the point where x = 0. Verify these features on your graph.

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = 9 - x²

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Key Concepts

Quadratic Functions

Vertex of a Parabola

Graphing Points