Question

Sketch a parabola with an axis of symmetry, y-intercept 1, and point (1, -5).

Answer 1

Sketching a parabola with a y-intercept of 1 and passing through the point (1, -5) involves plotting these points, determining and drawing the axis of symmetry at x=1, and completing the parabola shape by reflecting across the axis of symmetry.

Step-by-step explanation:

To sketch a parabola with the given properties, i.e., an axis of symmetry, a y-intercept of 1, and passing through the point (1, -5), you can follow these steps:

1. Plot the y-intercept by placing a point at (0, 1) on the y-axis.
2. Plot the given point by placing a dot at (1, -5) on the graph.
3. Find the axis of symmetry. Since a parabola is symmetric with respect to the vertical line that goes through its vertex, and given the point (1, -5), we can assume that the axis of symmetry passes through x=1. This means our parabola opens either up or down.
4. Determine the direction the parabola opens. Since the y-value at x=1 is less than the y-intercept, the parabola must open downwards.
5. Draw a smooth curve through the point (1, -5) that slopes downwards as it moves away from this point and upwards as it approaches the y-intercept to complete the parabola.

Remember to make your parabola symmetric about the line x=1.