Answer:
The pair of equations that generates graphs
with the same vertex is :
y = –4x² ; y = 4x²
Explanation:
A quadratic function can be written in the form f(x) = a(x – h)² + k, where a, h, and k are constants.
It’s graph is a parabola which has a vertex at (h, k).
• 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 different 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 the same 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 different 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 different vertices.