Writing equations for parabolas?

For your parabolas:

1. vertex at (- 2, 3). substituting these values for h and k:

y = (x + 2)^2 + 3

2. vertex at (2, 6). substituting these values for h and k:

y = (x - 2)^2 + 6

Note, you do not need to find the other variables.

1. It has the vertex of (-2,3); opens upward?

y = a(x - -2)² + 3

y = a(x + 2)² + 3

where a > 0

2. It has the vertex at (2, 6); opens upward?

y = a(x - 2)² + 6

y = a(x - 2)² + 6

where a > 0

y = a(x-h)² + k is the equation of a vertical parabola with vertex (h, k).

If a < 0 then the parabola opens downwards.

If a > 0 then the parabola opens upwards.

up-opening parabola with vertex (-2, 3):

y = a(x+2)² + 3, a>0

up-opening parabola with vertex (2, 6):

y = a(x-2)² + 6, a>0

Three important rules:

When h is positive the graph shifts right; when h is negative the graph shifts left.

When k is positive the graph shifts up; when k is negative the graph shifts down.

The vertex is (h, k) and the axis of symmetry is the line x = h.

To your parabolas:

#1 vertex at (- 2, 3). substituting these values for h and k:

y = (x + 2)^2 + 3

#2 vertex at (2, 6). substituting these values for h and k:

y = (x - 2)^2 + 6

To answer this question you need to realize that the sign of 'a' will determine whether the votex opens upwards or downwards. If 'a' has a negative value the parabola will open downward and be shaped like an umbrella. If it is positive it will open upwards and be shaped like a bowl.

There is nothing in your question that would make 'a' negative therefore they both open upwards.

(h, k ) is the vertex, opens up means a is positive.

y=(x+2)^2 + 3

y=(x-2)^2 + 6