1. Section 2.1 Transformations of Quadratic Functions
Honors Algebra 2
Section 2.1
Transformations of Quadratic Functions

2. Essential Question
How do the constants a, h and k transform the parent quadratic function graph?
𝑦= 𝑥 𝑦=𝑎 (𝑥−ℎ) 2 +𝑘

3. The graph of a quadratic function is a parabola.
Do exploration 1 on page 47 with a partner

4. Translations “h” and “k” move the parabola horizontally or vertically
The size and shape of the parabola does NOT change.
Recall the jingle:
Add to x, go _______
Add to y, go _______

5. This quadratic function is
written in vertex form.
It is very easy to figure out
what the vertex is. Different
values of “a” do not
change the vertex.

6. Reflections
If x is replaced with a negative x, the graph flips across the y axis. The graph looks exactly the same.
If y (f(x)) is replaced with a negative y, the graph flips across the x axis. In other words, “a” is negative. You have a sad face parabola.

7. Stretches and shrinks “a” changes the shape of the parabola
When a is greater than 1, you have a “skinny” parabola
When the absolute value of a is between 0 and 1, you have a “chubby” parabola

8. For the parent quadratic function, the vertex (turning point) is at (0,0)
When the function is transformed, the vertex may change. The new vertex is at (h,k).

9. Writing a transformed quadratic function using the parent function
Write a transformation function that is translated 4 units left and 3 units down, followed by a reflection in the y axis.
Do the translation 1st.
Then flip the graph.

10. Challenge
You can also transform a function that is not the parent function!
𝑓 𝑥 =4 𝑥 2 −3
Write a new function g that is translated 1 unit to the right followed by a reflection in the y-axis.

11. Standard form of a quadratic function
The standard form equation looks like this:
𝒚=𝒂 𝒙 𝟐 +𝒃𝒙+𝒄
To make the change
-square the binomial (remember FOIL?)
-combine like terms

12. Real life
Think of some real life examples of parabolas!

14. When an object is thrown or shot upward, gravity takes over and it follows a parabolic curve.
ℎ 𝑡 =−𝑔 𝑡 2 + 𝑣 0 𝑡+ ℎ 𝑜
g=4.9 (when units are in meters)
g=16 (when units are in feet)
t=time
h(t)=height
𝑣 0 =initial velocity
ℎ 0 =initial height
𝑣 0

15. http://phet. colorado. edu/sims/projectile-motion/projectile-motion_en

16. Assignment #5
Pg. 52 #1-11 odd, all, odd, 43, 44