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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