For each equation, write the coordinates of the vertex of the graph that represents the equation.

1. \(y=(x-3)^2 + 5\)
2. \(y=(x+7)^2 + 3\)
3. \(y=(x-4)^2\)
4. \(y=x^2 - 1\)
5. \(y=2(x+1)^2-5\)
6. \(y=\text-2(x+1)^2-5\)

For each function, write the coordinates of the vertex of its graph, and tell whether the graph opens upward or downward.

Here is a graph that represents \(y = x^2\).

1. Describe what would happen to the graph if the original equation were modified as follows:

   1. \(y=\text-x^2\)
   2. \(y=3x^2\)
   3. \(y=x^2 + 6\)

   

   A curve in an x y plane, origin O. Horizontal axis, scale negative 8  to 8, by 2’s. Vertical axis, scale negative 12 to 12, by 2’s. A curve, labeled y equals x squared, passes through the points negative 2 comma 4, 0 comma 0, and 2 comma 4.

2. Sketch the graph of the equation \(y=\text-3x^2 + 6\) on the same coordinate plane as \(y=x^2\).

Here are four graphs. Match each graph with a quadratic equation that it represents.

A curve in an x y plane, origin O. Horizontal axis, scale negative 6  to 4, by 1’s. Vertical axis, scale negative 4 to 4, by 1’s. A curve passes through the points 1 comma 0, 2 comma negative 1, 3 comma 0.

A curve in an x y plane, origin O. Horizontal axis, scale negative 6  to 4, by 1’s. Vertical axis, scale negative 4 to 4, by 1’s. A curve passes through the points negative 1 comma 0, negative 2 comma negative 1, negative 1 comma 0.

A curve in an x y plane, origin O. Horizontal axis, scale negative 6  to 4, by 1’s. Vertical axis, scale negative 4 to 4, by 1’s. A curve passes through the points negative 1 comma 2, 3 comma negative 0, 1 comma 2.

A curve in an x y plane, origin O. Horizontal axis, scale negative 6  to 4, by 1’s. Vertical axis, scale negative 4 to 4, by 1’s. A curve passes through the points negative 1 comma negative 2, 0 comma negative 3, and 1 comma negative 2.