Question

Write a possible equation for the following graph using transformations. Point is (-2,0) and (0,2)

Answer 1

One possible equation for the graph can be expressed as:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola. We can determine the values of a, h, and k using the given points (-2,0) and (0,2).

Let's start with the x-coordinate of the vertex, which is h. We can find it as the average of the x-coordinates of the given points:

h = (x₁ + x₂) / 2
h = (-2 + 0) / 2
h = -1

Similarly, we find the y-coordinate of the vertex, k, as the average of the y-coordinates of the given points:

k = (y₁ + y₂) / 2
k = (0 + 2) / 2
k = 1

Now we can substitute the values of h and k into the equation to get:

y = a(x - (-1))² + 1
y = a(x + 1)² + 1

Next, we can use one of the points, (-2,0), to determine the value of a. Substituting the coordinates into the equation yields:

0 = a((-2) + 1)² + 1
0 = a(1)² + 1
0 = a + 1

Solving for a, we subtract 1 from both sides:

a = -1

Substituting the value of a back into the equation, we get the final equation:

y = -1(x + 1)² + 1

Therefore, one possible equation for the given graph is y = -1(x + 1)² + 1.