Parabola Party Hosted by Quadratic Functions All Others

Parabola Party: Hosted by Quadratic Functions, All Others Welcome! MATH II UNIT 1 Come On Ride The Train!

What we should already know about quadratic functions…

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Have you seen these parabolic shapes before?

The train is my DOMAIN! This train travels from left to right along the xaxis. Our domain is the set of all x-values that are covered by the function.

The DOMAIN of any quadratic function is all real numbers. Another way to write this is from (-∞, ∞).

The RANGE of a quadratic function in the upright position goes from the y-value of the vertex to ∞. The RANGE of a quadratic function in the downward goes from -∞ to y-value of vertex.

How low can you go? RANGE is read from bottom to top and is on the y-axis. How high can you fly?

Standard form of a Quadratic Function 2 y = ax + bx + c

Shape of a quadratic function The shape of a quadratic is a parabola. It can open up or down.

Vertical Stretch y = x 2 y = 3 x 2 The vertical stretch is caused by the “a” value being greater than 1. It will make the graph look tall and skinny when compared to the parent function.

Vertical Shrink y = x 2 y = 0. 5 x 2 The vertical shrink is caused by the “a” value being between 0 and 1 (fraction or decimal with no whole part). It will make the graph look short and fat when compared to the parent function.

Vertical Shift y = x 2 + 3 y = x 2 - 3 The vertical shift is caused by a value being added or subtracted to the parent function equation. It will make all points move up or down from the original points of the parent function.

Reflection across the x-axis y = x 2 y = -x 2 The reflection across the x-axis is caused by a negative being placed in front of the “a” value. When compared to the parent function, all values are the opposite of the parent function values.

Multiple Transformations in a Graph y = x 2 y = 2 x 2 - 1 Compare the two equations. What was changed from the parent function to the new function? We know that the 2 before the x 2 causes the graph to become tall and skinny because it is a vertical stretch. The 1 being subtracted from the x 2 causes the graph to move down one unit because it is a vertical shift down.

Multiple Transformations in a Graph y = x 2 y = -0. 5 x 2 + 3 Compare the two equations. What was changed from the parent function to the new function? Discuss with your partner the transformations seen in the red function.

Skill Sheet Example Set 1 y = x 2 + 1 Explanation: y = 3 x 2 – 2 Explanation: y = 0. 2 x 2 – 1 Explanation: