Question

What is the vertex form of the graphed equation?

(1 point)
Responses

y=2(x−4)2+8
𝑦
=
2
(
𝑥
−
4
)
2
+
8
y equals 2 left parenthesis x minus 4 right parenthesis squared plus 8

y=−2(x−4)2+8
𝑦
=
−
2
(
𝑥
−
4
)
2
+
8
y equals negative 2 left parenthesis x minus 4 right parenthesis squared plus 8

y=2(x+4)2+8
𝑦
=
2
(
𝑥
+
4
)
2
+
8
y equals 2 left parenthesis x plus 4 right parenthesis squared plus 8

y=2(x−4)2−8

Answer 1

The vertex form of a parabolic equation is generally expressed as \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola and \(a\) determines the direction and width of the parabola.

To determine which option represents the correct vertex form from the responses provided:

1. **Option 1: \(y = 2(x - 4)^2 + 8\)** has a vertex at (4, 8).
2. **Option 2: \(y = -2(x - 4)^2 + 8\)** has a vertex at (4, 8) as well but opens downwards.
3. **Option 3: \(y = 2(x + 4)^2 + 8\)** has a vertex at (-4, 8).
4. **Option 4: \(y = 2(x - 4)^2 - 8\)** has a vertex at (4, -8).

To choose the appropriate equation, you would typically be given a graph or additional details about the vertex or direction of opening (upwards or downwards) of the parabola.

If the graph has a vertex at (4, 8) and opens upwards, then the correct response would be:

**y = 2(x - 4)^2 + 8**.