Question

1. identify the vertex of the function ( y = (x - 1)^2 - 16 ) and then use a table of values to identify two ordered pairs on either side of the vertex.

• the vertex is ( (1, -16) ). the ordered pairs are ( (-3, -32) ), ( (-1, -20) ), ( (3, -12) ), and ( (5, 0) ).
• the vertex is ( (1, -16) ). the ordered pairs on either side of the vertex are ( (-3, 0) ), ( (-1, -12) ), ( (3, -12) ), and ( (5, 0) ).
• the vertex is ( (-1, 16) ). the ordered pairs on either side of the vertex are ( (-3, 0) ), ( (-1, -12) ), ( (3, -12) ), and ( (5, 0) ).
• the vertex is ( (-1, -16) ). the ordered pairs on either side of the vertex are ( (-3, 0) ), ( (-1, -12) ), ( (3, -12) ), and ( (5, 0) ).

Explanation:

Step1: Identify the vertex form of a parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For the function \( y = (x - 1)^2 - 16 \), we compare it with the vertex form. Here, \( h = 1 \) and \( k = -16 \), so the vertex is \((1, -16)\).

Step2: Check the ordered pairs

Let's substitute the x - values of the ordered pairs into the function \( y=(x - 1)^2-16 \) to verify:

• For \( x=-3 \): \( y=(-3 - 1)^2-16=(-4)^2-16 = 16 - 16=0 \)
• For \( x=-1 \): \( y=(-1 - 1)^2-16=(-2)^2-16 = 4 - 16=-12 \)
• For \( x = 3 \): \( y=(3 - 1)^2-16=(2)^2-16 = 4 - 16=-12 \)
• For \( x = 5 \): \( y=(5 - 1)^2-16=(4)^2-16 = 16 - 16=0 \)

These values match the ordered pairs given in the third option. Also, the vertex \((1,-16)\) is correctly identified in the third option.

Answer:

The third option (The vertex is (1, −16). The ordered pairs on either side of the vertex are (−3, 0), (−1, −12), (3, −12), and (5, 0))