Answer the three questions below about the quadratic equation y=(x-4)^2-7.

What is the vertex?
Choices:
(-4,-7)
(-4,7)
(4,-7)
(4,7)
What is the axis of symmetry?
Choices:
x=4
x=-4
x=7
x=-7
What is the minimum or maximum point of the graph?
Choices:
Maximum at -7
Maximum at -4
Minimum at -7
Minimum at -4

1 answer

To analyze the quadratic equation \( y = (x - 4)^2 - 7 \), we can gather the information as follows:

Vertex: The vertex form of a quadratic equation is given by \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, \( h = 4 \) and \( k = -7\). Therefore, the vertex is (4, -7).
Axis of Symmetry: The axis of symmetry for a quadratic in vertex form is the vertical line that passes through the vertex, which is given by \( x = h \). Since \( h = 4 \), the axis of symmetry is x = 4.
Minimum or Maximum Point: The coefficient of the squared term, \( (x - 4)^2 \), is positive (1 in this case), indicating that the parabola opens upwards. This means the vertex represents a minimum point. Since \( k = -7 \), the minimum point is Minimum at -7.

To summarize:

Vertex: (4, -7)
Axis of Symmetry: x = 4
Minimum or Maximum: Minimum at -7