Question

Can someone please help me

Answer 1

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:

$\displaystyle\mathsf{\frac{9}{9}\:=\:\frac{9a}{9}}$

a = 1

Final answer:

Therefore, the vertex form of the given parabola is: y = a(x + 1)² - 9.

Answer 2

It’s y = (x + 1) ^2 - 9