Find the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2-x^2
To find the line of symmetry, maximum or minimum value, and graph the quadratic function f(x) = 2 - x^2, we can start by finding the vertex of the parabola.
The vertex form of a quadratic equation is f(x) = a(x-h)^2 + k, where (h,k) represents the vertex.
In our case, a = -1, h = 0, and k = 2. Thus, the vertex of the parabola is (0, 2).
The line of symmetry for a parabola is a vertical line that passes through its vertex. In this case, the line of symmetry is x = 0.
To find the maximum or minimum value of the quadratic function, we can observe that since the coefficient of the x^2 term is -1, the parabola opens downwards, which means its vertex represents the maximum point. Therefore, the maximum value is f(0) = 2.
Now, let's graph the function f(x) = 2 - x^2:
We'll start by plotting the vertex at (0, 2).
Next, let's choose some x values on both sides of the vertex and substitute them into the equation to find the corresponding y values. For example, when x = -1, y = 2 - (-1)^2 = 1. Similarly, when x = 1, y = 2 - 1^2 = 1.
Plot these points on the graph, (-1, 1) and (1, 1).
Lastly, draw a smooth curve that passes through the vertex and the plotted points. The shape of the graph should resemble a downward-opening parabola with its vertex at (0, 2) and passing through (-1, 1) and (1, 1).
The graph of the function f(x) = 2 - x^2 should look like this:
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-3 -2 -1 0 1 2 3