y=x²
In this equation, y equals x squared (y = x²)
In this equation, y equals x squared (y = x²). This is a quadratic equation, as it includes a squared term (x²).
To understand its graph, we can create a table of values by choosing x-values and calculating the corresponding y-values. Let’s choose some x-values: -2, -1, 0, 1, and 2.
When x = -2: y = (-2)² = 4
When x = -1: y = (-1)² = 1
When x = 0: y = (0)² = 0
When x = 1: y = (1)² = 1
When x = 2: y = (2)² = 4
Now, plot these points on the Cartesian plane with x as the horizontal axis and y as the vertical axis. You’ll notice that the graph of y = x² is a symmetric and smooth curve that opens upwards. It passes through the point (0, 0) which is called the vertex.
The graph extends indefinitely on both sides, approaching infinity as x approaches both positive and negative infinity. It has a minimum value of 0, as the square of any real number is never negative. Furthermore, the graph is concave up, meaning that its curvature opens upwards.
It is important to note that the graph of y = x² is a parabola. The term “parabola” refers to the general shape of the graph, which resembles an arch or a U-shape.
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