Quadratic Transformations Practice Problems

Here you will find a collection of basic quadratic transformations practice problems. Visit this page directly at hunkim.com/quadratictransformations

1. Sketch f(x)=x^2 and label 3 points.
   
   
2. f(x)=x^2
   1. Sketch y=x^2+2
      
      
   2. Sketch y=x^2-4
      
      
   3. Sketch f(x)=x^2-5
      
      
   4. Sketch g(x)=f(x)-1
      
      
   5. Sketch g(x)=f(x-2)
      
      
   6. Sketch y=f(x+3)
      
      
   7. Sketch h(t)=\left(t-\frac{1}{2}\right)
      
      
   8. Sketch y=-f(x)
      
      
   9. Sketch y=2f(x)
      
      
   10. Sketch y=-\frac{1}{2}f(x-2)
       
       
3. Sketch y=2x^2 and label 3 points.
   
   
4. Create a table of values for g(x)=2(x-1)^2+3 and sketch 3 points.
   
   
5. f(x)=x^2. Find the actual equation of:
   1. g(x)=f(x-1)+2
      
      
   2. g(x)=2f(x)-3
      
      
   3. g(x)=-\frac{2}{3}f(x+3)-\frac{1}{2}
      
      
   4. g(x)=2f(x-2)+1.
      
      
6. f(x)=x^2-3x
   1. Sketch y=f(x)
      
      
   2. Given g(x)=2f(x-2), what is the actual equation of g(x)?
      
      
      Click here to practice more function substitution.
      
      
7. f(x)=x^2 and g(x)=af(x-b)+c
   1. What are the effects of the parameters a, b, and c?
      
      
   2. Does order matter? Which transformation should be applied first? Stretches and flips or horizontal and vertical shifts?
      
      
8. f(x)=x^2
   1. g(x)=9f(x) and h(x)=f(3x). Show that h(x)=g(x).
      
      
9. Absolute value transformations: f(x)=-x(x-2).
   1. Sketch g(x)=|f(x)|
      
      
   2. Sketch h(x)=f\left(|x|\right)
      

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