Graph parabolas

how would i do this

y=x^2 + 1 (-3 < or equal to X < or equal to 3)

To graph a parabola, you can follow these steps:

1. Determine the vertex: The vertex of the parabola is given by the coordinates (h, k). In this case, the equation is y = x^2 + 1, which is in the standard form y = a(x - h)^2 + k. Comparing the equation to the standard form, we can see that h = 0 and k = 1. So, the vertex is (0, 1).

2. Determine the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. For this parabola, it is the line x = 0.

3. Find the y-intercept: The y-intercept is the point where the parabola intersects the y-axis. To find this, substitute x = 0 into the equation and solve for y. In this case, when x = 0, y = 0^2 + 1 = 1. So, the y-intercept is (0, 1).

4. Determine other points: Choose some values for x within the given range (-3 ≤ x ≤ 3), and plug them into the equation to find the corresponding y-values. For example, when x = -3, y = (-3)^2 + 1 = 9 + 1 = 10. So one point on the parabola is (-3, 10). Similarly, when x = 3, y = 3^2 + 1 = 9 + 1 = 10. This gives us another point of (3, 10).

5. Sketch the graph: Plot the vertex, the y-intercept, and any other points you found on the graph. Then, draw a smooth curve that passes through these points. Since the parabola is symmetrical, you can reflect the points on one side of the axis of symmetry to the other side to complete the graph.

In this case, the vertex is (0, 1), the y-intercept is (0, 1), and the points (-3, 10) and (3, 10) lie on the parabola. After plotting these points and drawing a smooth curve passing through them, you will have graphed the parabola y = x^2 + 1 within the range -3 ≤ x ≤ 3.