Answer:
Option 2: y = a(x + 1)² - 9
Step-by-step explanation:
Given the graph of an upward-facing parabola, whose vertex occurs at point (-1, -9) as its minimum point.
Vertex Form
Using the vertex form of the quadratic equation, y = a(x - h)² + k:
where:
a = determines the wideness and the direction of where the graph opens.
(h, k) = vertex
h = determines the horizontal translation of the graph
k = determines the vertical translation of the graph
Using the vertex, (-1, -9), and another point from the graph, (2, 0), substitute these values into the vertex form to solve for the value of a:
y = a(x - h)² + k
0 = a[2 - (-1)]² - 9
0 = a(2 + 1)² - 9
0 = a(9) - 9
Add 9 to both sides to isolate a:
0 + 9 = 9a - 9 + 9
9 = 9a
Divide both sides by 9 to isolate a:
[tex]\displaystyle\mathsf{\frac{9}{9}\:=\:\frac{9a}{9}}[/tex]
a = 1
Final answer:
Therefore, the vertex form of the given parabola is: y = a(x + 1)² - 9.
