1. Where is the vertex of the graph that represents \(y=(x-2)^2 -8\)?
2. Where is the \(y\)-intercept? Explain how you know.
3. Identify one other point on the graph of the equation. Explain or show how you know.
4. Sketch a graph that represents the equation.

   

Function \(v\) is defined by \(v(x)=\frac12(x+5)^2 - 7\).

Without graphing, determine if the vertex of the graph representing \(v\) shows the minimum or maximum value of the function. Explain how you know.

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

1. Describe what would happen to the graph if the original equation was changed to:
   1. \(y=\frac12 x^2\)
   2. \(y=x^2-8\)

   

   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. Graph the equation \(y=\frac12 x^2-8\) on the same coordinate plane as \(y=x^2\).

Technology required. Two objects are launched into the air.

• The height, in feet, of Object A is given by the equation \(f(t)=4+32t-16t^2\).
• The height, in feet, of the Object B is given by the equation \(g(t)=2.5+40t-16t^2\). In both functions, \(t\) is seconds after launch.

Use technology to graph each function in the same graphing window.

1. What is the maximum height of each object?
2. Which object hits the ground first? Explain how you know.

Andre thinks the vertex of the graph of the equation \(y=(x+2)^2-3\) is \((2,\text-3)\). Lin thinks the vertex is \((\text-2,3)\). Do you agree with either of them?