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Anettt [7]
11 months ago
11

Which pair of equations generates graphs with the same vertex?

Mathematics
2 answers:
puteri [66]11 months ago
6 0

Answer:

The pair of equations that generates graphs

with the same vertex is :

y = –4x²   ;    y = 4x²

Step-by-step explanation:

<u><em>A quadratic function can be written in the form  f(x) = a(x – h)² + k, where a, h, and k are constants. </em></u>

<u><em>It’s graph is a parabola which has a vertex at (h, k).</em></u>

• The graph of the equation y = – (x + 4)² = – [x – (–4)]² + 0

has a vertex at (-4 , 0).

On the other hand ,The graph of the equation y = (x – 4)² = (x – 4)² + 0

has a vertex at (4 , 0).

Therefore , the two equations generate graphs with <u>different</u> vertices.

• The graph of the equation y = –4x² = –4 (x –0)² + 0

has a vertex at (0 , 0).

On the other hand ,The graph of the equation y = 4x² = 4 (x –0)² + 0

has a vertex at (0 , 0).

Therefore , the two equations generate graphs with <u>the same</u> vertex.

• The graph of the equation y = – x² – 4 = – (x – 0)² + (– 4)

has a vertex at (0 , -4).

On the other hand ,The graph of the equation y = x² + 4 = (x – 0)² + 4

has a vertex at (0 , 4).

Therefore , the two equations generate graphs with <u>different</u> vertices.

• The graph of the equation y = (x – 4)² = (x – 4)² + 0

has a vertex at (4 , 0).

On the other hand ,The graph of the equation y = x² + 4 = (x – 0)² + 4

has a vertex at (0 , 4).

Therefore , the two equations generate graphs with <u>different</u> vertices.

zvonat [6]11 months ago
5 0

Answer:

D

Step-by-step explanation:

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