Unit 4, Lesson 17
Changing the Vertex
Integrated Math 2
17.1
Warm-up
Graphs of Two Functions
Here are graphs representing two functions, Two graphs representing functions in x y plane, origin O. First graph opens upward, crosses the negative x axis in two places, and crosses the y axis above the origin. Second graph opens upward, crosses the x axis with one negative point and the other at the origin.
- Which graph represents each function? Explain how you know.
- Where does the graph of
meet the -axis? Explain how you know.
17.4
Activity
Smiley Face
Do you see 2 “eyes” and a smiling “mouth” on the graph? The 3 arcs on the graph all represent quadratic functions that were initially defined by
- Write equations to represent each curve in the smiley face.
- What domain is used for each function to create this graph?
Student Lesson Summary
The graphs of
Three parabolas in x y plane, origin O. X axis negative 8 to 8, by 2’s. Y axis negative 20 to 30, by 10s. First parabola labeled y equals x squared opens upward with vertex at the origin. Second parabola labeled y equals x squared plus 12 opens upward with a vertex at 0 comma negative 12. Third parabola labeled y equals open parenthesis, x plus 3, end parenthesis, squared opens upward with a vertex at negative 3 comma 0.
Notice that adding 12 to
We can also shift a graph both horizontally and vertically.
The graph that represents
Two parabolas in x y plane, origin O. X axis negative 8 to 8, by 2’s. Y axis negative 20 to 30, by 10s. First parabola labeled y equals x squared opens upward with vertex at the origin. Second parabola labeled y equals open parenthesis, x plus 3, closed parenthesis, squared, plus 12 opens upward with a vertex at negative 3 comma 12.
The graph representing the equation
Two parabolas in x y plane, origin O. X axis negative 8 to 2, by 2’s. Y axis negative 20 to 20, by 20s. Parabola labeled y equals open parenthesis, x plus 3, closed parenthesis, squared, plus 12 opens upward. Parabola labeled y equals negative open parenthesis, x plus 3, end parenthesis, squared, plus 12 opens downward.
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