Mastering Quadratic Functions: Graphing the Quadratic Parent Function f(x) = x^2

Graph of Quadratic Parent Function

The graph of a quadratic parent function is a U-shaped curve called a parabola

The graph of a quadratic parent function is a U-shaped curve called a parabola. The standard form of a quadratic parent function is f(x) = x^2.

To graph this function, we can start by choosing some x-values and plugging them into the equation to find the corresponding y-values. Let’s choose x-values of -2, -1, 0, 1, and 2:

When x = -2, f(x) = (-2)^2 = 4
When x = -1, f(x) = (-1)^2 = 1
When x = 0, f(x) = (0)^2 = 0
When x = 1, f(x) = (1)^2 = 1
When x = 2, f(x) = (2)^2 = 4

Now, we can plot these points on a coordinate grid. The x-values go on the x-axis and the corresponding y-values go on the y-axis. So, the points we have are (-2, 4), (-1, 1), (0, 0), (1, 1), and (2, 4).

Next, we can draw a smooth curve that passes through these points. Since it’s a U-shaped curve, we can start at the lowest point, which is the vertex of the parabola. In this case, the vertex is at (0, 0).

Now, to determine the shape of the parabola, we can observe that the coefficient of x^2 is positive (in this case, 1), which means the parabola opens upwards. If the coefficient were negative, the parabola would open downwards.

With this information, we can continue drawing the curve, making sure it is symmetrical about the vertical line passing through the vertex. The curve will approach the x-axis as it moves away from the vertex.

Once we have plotted enough points and drawn the parabola using a smooth curve, we have completed the graph of the quadratic parent function f(x) = x^2.

I hope this helps! Let me know if you have any further questions.

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