Vertical Stretches and Reflections

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Vertical Stretches and Reflections
Recall that the vertex form of a quadratic equation is y=a(x−h)2+ky=a\left(x-h\right)^2+ky=a(x−h)2+k. Let's explore how these different numbers a, h, and ka,\ h,\ \text{and}\ ka, h, and k affect the graph.

The graphs of y=ax2\bm{\colorOne{y=ax^2}}y=ax2
Based on the following graphs, try to identify the role aaa plays in graphing a quadratic graph.

Write it Down
How does the aaa value affect the graph of y=ax2\bm{y=ax^2}y=ax2?
If aaa is positive, the graph           opens up          
If aaa is negative, the graph           opens down          
The transformation is                     a vertical reflection along the x-axis                    
If a>1a>1a>1 or a<−1a<-1a<−1, the graph                     is stretched so it's longer                    
If 0<a<10<a<10<a<1 or −1<a<0-1<a<0−1<a<0, the graph                     is compressed (shrunk) so it's shorter                    
The transformation is                     a vertical stretch or compression                    

Practice: Vertical Reflections
Select all of the equations that results in a parabola (U-shape) that opens down.

A) y=x2−3y=x^2-3y=x2−3

B) y=−x2−3y=-x^2-3y=−x2−3

C) y=−2x2y=-2x^2y=−2x2

D) y=2(x−2)2+1y=2(x-2)^2+1y=2(x−2)2+1

E) y=−0.5(x+1)2−5y=-0.5(x+1)^2-5y=−0.5(x+1)2−5

F) y=−34(x−1)2+53y=-\frac{3}{4}(x-1)^2+\frac{5}{3}y=−43​(x−1)2+35​

I don't know

Practice: Vertical Stretch & Compressions
For each of the following equations, identify the type of vertical stretch or compression that is being applied (if there are any)

y=2(x+3)2−5y=2(x+3)^2-5y=2(x+3)2−5

A) Vertical stretch by a factor of 222

B) Vertical compression by a factor of 12\dfrac{1}{2}21​

C) Vertical stretch by a factor of 5

D) Vertical compression by a factor of 15\dfrac{1}{5}51​

E) Neither stretch nor compression

I don't know

Wize High School Grade 11 Math Textbook > Vertex Form of a Quadratic Equation

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Vertical Stretches and Reflections

The graphs of $\bm{\colorOne{y=ax^2}}$

Practice: Vertical Reflections

Practice: Vertical Stretch & Compressions