Unit 7, Lesson 17
Changing the Vertex
Algebra 1
Practice
Problem 1
Here is the graph of quadratic function \(f\).
Andre uses the expression \((x-5)^2+7\) to define \(f\).
Noah uses the expression \((x+5)^2-7\) to define \(f\).
Do you agree with either of them? Explain your reasoning.
Problem 2
Here are the graphs of \(y=x^2\), \(y=x^2-5\), and \(y=(x+2)^2-8\).
- How do the 3 graphs compare?
Three parabolas in x y plane, origin O. X axis negative 10 to 4, by 2’s. Y axis negative 12 to 12, by 4s. First parabola labeled y equals x squared opens upward with vertex at the origin. Second parabola labeled y equals x squared minus 5 opens upward with a vertex at 0 comma negative 5. Third parabola labeled y equals open parenthesis, x plus 2, end parenthesis, squared, minus 8 opens upward with a vertex at negative 2 comma negative 8.
- Compare the graphs of \(y=x^2\) and \(y = x^2-5\). What role does the -5 play in the comparison?
- Compare the graphs of \(y=x^2\) and \(y=(x+2)^2-8\). What role do the 2 and 8 play in the comparison?