Answer:
Axis of symmetry: x = 5
Vertex form: y = -4(x - 5)² + 3
Step-by-step explanation:
Given ordered pairs: (2, -33) (3, -13) (4, -1) (5, 3) (6, -1)
Axis of Symmetry
As this is a parabola, it will be symmetrical.
To determine the axis of symmetry, identify two ordered pairs that have the same y-values and find their midpoint.
Two ordered pairs with the same y-value: (-4, 1) and (6, -1)
Midpoint of x = 4 and x = 6 is: x = 5
Therefore, the axis of symmetry is x = 5
Vertex form
Vertex form of a quadratic equation: y = a(x - h)² + k
(where (h, k) is the vertex)
The axis of symmetry is the x-value of the vertex of the parabola.
As we have been given the point when x = 5, the vertex is: (5, 3)
Substituting this into the formula:
⇒ y = a(x - 5)² + 3
To find the value of a, substitute any of the other points into the formula and solve for a.
Using (4, -1)
⇒ a(4 - 5)² + 3 = -1
⇒ a(-1)² = -4
⇒ a = -4
Therefore, the vertex form of the parabola is:
y = -4(x - 5)² + 3
