y= x^2
Quadratic parent function (parabola)
The equation y = x^2 represents a quadratic function. In this equation, x is the independent variable, and y is the dependent variable. The equation states that the value of y is determined by squaring the value of x.
Graphically, the equation represents a parabola opening upwards. As x increases, the values of y also increase, but at a faster rate due to the squaring function. The vertex of the parabola is located at the origin (0,0), and the parabola is symmetric about the y-axis.
To find specific points on the graph, you can substitute different values of x into the equation. For example, if you substitute x = 1, you get y = 1^2 = 1. So, the point (1, 1) lies on the graph. Similarly, if you substitute x = -2, you get y = (-2)^2 = 4. Therefore, the point (-2, 4) also lies on the graph.
You can also find the x-intercepts (where the graph intersects the x-axis) by setting y equal to zero and solving for x. In this case, you would set x^2 = 0, which implies that x = 0. So, the graph intersects the x-axis at the point (0, 0).
In summary, the equation y = x^2 represents a quadratic function in which the value of y is related to the square of x. The graph of this equation is a symmetric parabola with its vertex at the origin.
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