MATH II UNIT 1 Parabola Party: Hosted by Quadratic Functions, All Others Welcome!

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Presentation transcript:

MATH II UNIT 1 Parabola Party: Hosted by Quadratic Functions, All Others Welcome!

What we should already know about quadratic functions…

The shape of a quadratic function, the parabola, is seen almost everyday, but do you realize it?

Have you seen these parabolic shapes before?

The train is my DOMAIN! This train travels from left to right along the x- axis. 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 y = ax 2 + 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 = 3x 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 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. y = x 2 y = 0.5x 2

Vertical Shift y = x 2 y = x y = x 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 = 2x 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 = -0.5x 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 Explanation: y = 3x 2 – 2 Explanation: y = 0.2x 2 – 1 Explanation: