NAME Lauren ferber STUDENT HANDOUT MATH 100 LAB 20 INSTRUCTOR ELDER For each of the following quadraticfunctions, find the vertex and thex-intercept(s) of its graph. If the graph has nox-intercepts be sure to indicate that they do not exist by writing NONĚ in the blank. 1. f(x)=x+9 Vertex x-intercept(s) 2. f(x) =x-6x Vertex X-intercept(s) 2. 3. f( x) =x-4x Vertex x-intercept(s) 4. f( x)=2x²+7x-4 Vertex x-intercept(s) 5. f(x)=16x-64 Vertex x-intercept(s) 6. f(x)=x-4x-21 Vertex x-intercept(s)

The data in the table shows the number of mother-to-child HIV infections diagnosed in the United States in various years from 1985 to 2005. How can we learn from the data? Practice the following questions: 1. Make a scatter plot to display the data. You can use any graphing technology. Why would a quadratic model make sense? 2. Determine an equation for this relation. Which form (standard, vertex or factored) do you think is the best for these data and why? 3. Based on your model, will the number of HIV cases ever be reduced to zero? If so, when? Explain reasoning.

For the following equation, find the vertex and determine if it is a maximum or minimum point, find the y-intercept and the zeros if they exist. y = x^2+6x+9

Determine the maximum or minimum value for each quadratic relation below. a) y = 2 (x - 5)^2 - 8 b) y = -3 (x + 7)^2 +12