The parabola, with an axis of symmetry x = -2 and passing through (-5, 6), has another point at (1, 6), confirming its symmetry and providing a clear snapshot of its shape.
The axis of symmetry for a parabola is a vertical line given by x = h. In this case, the axis is x = -2, meaning the vertex is at (-2, k).
The parabola passes through the point (-5, 6). Since the vertex is on the axis of symmetry, its x-coordinate is also -5.
Using the vertex form y = a(x - h)^2 + k, substitute h = -2 and x = -5 to find k: 6 = a(-5 - (-2))^2 + k, which simplifies to 6 = 9a + k.
To find another point, choose a convenient x-value. Let's use x = 1 (on the other side of the vertex). Substitute this into the equation to get y = 9a + k.
Substitute k = 6 (from the given point), giving y = 9a + 6.
Now, we have two equations: 6 = 9a + k and y = 9a + 6.
Subtract the first equation from the second: y - 6 = 0, simplifying to y = 6.
Therefore, another point on the parabola is (1, 6).