Question 591
Different books actually have slightly different standard forms for the parabola. One version is:
{{{y = a(x - h)^2 + k}}} Where (h, k) is the vertex.

To find the y-intercept, just plug in zero for the x and solve for y.

To find two symmetrical points, find two numbers the same distance to the left and right of the x value of the vertex. Then plug them in for x and solve for y.

Example:
{{{y = (x - 2)^2 + 1}}} The vertex is (2, 1).

Plug in zero for x to find the y-intercept.
{{{y = (0 - 2)^2 + 1}}}
{{{y = (-2)^2 + 1}}}
y = 4 + 1
y = 5 So the y-intercept in point form is (0, 5).

Pick two x values that are the same distance from the x value of the vertex, such as 1 and 3. Then plug them into the equation to find the y values to go with them on the graph.
{{{y = (1 - 2)^2 + 1}}}
{{{y = (-1)^2 + 1}}}
y = 1 + 1
y = 2 So one point is (1, 2).

{{{y = (3 - 2)^2 + 1}}}
{{{y = (1)^2 + 1}}}
y = 1 + 1
y = 2 So a symmetrical point is (3, 2).

{{{graph(300, 200, -2, 6, -2, 10, (x - 2)^2 +1)}}}