Finding the Vertex, Axis of Symmetry, and Y-Intercept of the Quadratic Function f(x) = x²

f(x) = x²

Question: Find the vertex, axis of symmetry, and y-intercept of the function f(x) = x²

Question: Find the vertex, axis of symmetry, and y-intercept of the function f(x) = x².

Answer:
To find the vertex, axis of symmetry, and y-intercept of the function f(x) = x², we can use various properties and formulas related to quadratic functions.

1. Vertex: The vertex of a quadratic function in the form f(x) = ax² + bx + c can be found using the formula x = -b / (2a). In this case, our function is f(x) = x², so we have a = 1, b = 0, and c = 0. Plugging these values into the formula, we get x = -(0) / (2*1) = 0. Therefore, the vertex of the function is (0, 0).

2. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex of the quadratic function. For this particular function, the axis of symmetry is given by the equation x = 0, since the x-coordinate of the vertex is 0.

3. Y-intercept: The y-intercept is the point where the graph of the function intersects the y-axis. To find it, we set x = 0 in the original function and solve for y. Substituting x = 0 into f(x) = x², we get f(0) = 0² = 0. Therefore, the y-intercept is (0, 0).

In summary:
– Vertex: (0, 0)
– Axis of Symmetry: x = 0
– Y-intercept: (0, 0)

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