How to graph a parabola #y= 1/4(x-2)^2#?

Question

Eva Abramson · Accepted Answer

Problem: How to graph a parabola with the equation #y=1/4(x-2)^2# Simplify the equation. #y=((x-2)^2)/4# Make a table of #x# and #y# values. Include positive and negative values for #x#.
#color(red)x, color(blue)y#
#color(red)(-4),color(blue)9#
#color(red)(-2),color(blue)4#
#color(red)0,color(blue)1#
#color(red)2,color(blue)0#
#color(red)4,color(blue)1#
#color(red)6,color(blue)4# Plot the points and draw the parabola. graph{y=((x-2)^2)/4 [-16.03, 16, -8.01, 8.01]}

Kennedy Adams · Answer

undefined To graph the parabola y = 1/4(x - 2)^2:

1. Identify the vertex: The vertex of the parabola is at the point (2, 0).

2. Identify the axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 2.

3. Identify the direction of the parabola: Since the coefficient of x^2 is positive (1/4), the parabola opens upwards.

4. Plot additional points: Choose some x-values on either side of the vertex, plug them into the equation to find the corresponding y-values, and plot these points.

5. Sketch the parabola: Using the vertex and the additional plotted points, draw a smooth curve that represents the parabola.