Answer:
Option 2: y = a(x + 1)² - 9
Step-by-step explanation:
Given the graph of an upward-facing parabola, whose <u>vertex</u> occurs at point (-1, -9) as its minimum point.
<h2>Vertex Form</h2>Using the <u>vertex form</u> of the quadratic equation, y = a(x - h)² + k:
where:
<em>a</em> = determines the wideness and the direction of where the graph opens.
(h, k) = vertex
<em>h</em> = determines the horizontal translation of the graph
<em>k</em> = 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 <em>a</em>:
<h3>y = a(x - h)² + k</h3>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 <em>a:</em>
<em /><em />
<em>a </em>= 1
<h2>Final answer:</h2>Therefore, the <u>vertex form</u> of the given parabola is: y = a(x + 1)² - 9.
Given:
The quadratic equation is:
To find:
The value of k and .
Solution:
We have,
...(i)
Putting , we get
Putting in (i), we get
Splitting the middle term, we get
Here, and
.
Therefore, the required values are and
.