Quadratic Functions Practice Problems

Here you will find a concise collection of quadratic functions practice problems. Visit this page directly by visiting hunkim.com/quadratic

Formulas

• x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}
• x=-\frac{b}{2a}
• D=b^2-4ac
• y=a(x-b)^2+c

Factoring

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Completing the Square

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Quadratic Transformations

• Click here to practice basic transformations of quadratic functions or visit hunkim.com/quadraticTransformations
• Click here for more transformations practice problems.

Find the Equation of the Quadratic

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Quadratic Functions Practice Problems

1. f(x)=x^2-9
   1. Sketch and label 3 points
      
      
   2. Evaluate f(-2)
      
      
   3. Domain?
      
      
   4. Range?
      
      
   5. Coordinates of the vertex?
      
      
   6. Equation of the line of symmetry?
      
      
   7. Intercepts?
      
      
2. f(x)=-(x+2)(x-4).
   1. Sketch and label 3 points
      
      
   2. Evaluate f(2)
      
      
   3. Coordinates of the vertex?
      
      
   4. Equation of the line of symmetry?
      
      
   5. Intercepts?
      
      
   6. Given x\geq 2 find the range of f(x)
      
      
3. Enrichment: Complete the square on the general form of the quadratic equation: y=ax^2+bx+c.
   1. Why is x=-\frac{b}{2a} the equation of the line of symmetry?
      
      
   2. Can you see why x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}?
      
      
4. y=x^2-6x+8
   1. Solve by factoring
      
      
   2. Solve by using the quadratic formula
      
      
   3. Solve by completing the square
      
      
   4. When should you use each solving technique?
      
      
5. f(x)=-x^2+4x-3
   1. Write in the form a(x-h)^2+k.
      
      
   2. Hence solve the equation f(x)=-8.
      
      
6. Solve x^2=2x+8
   1. By sketching two graphs
      
      
   2. Graphically by sketching one graph
      
      
   3. Solve algebraically
      
      
7. Can you solve x^2+x-3 by factoring? If not, try another way.
   
   
8. Find the coordinates of the point of intersection of the graphs f(x)=(x-2)^2 and g(x)=-(x+1)^2+5.
   
   
9. y=(2x-3)(x+5)
   1. Solve the quadratic by observing the factors.
      
      
   2. Find the equation of the line of symmetry:
      1. Based on the roots
      2. By using the vertex formula
         
         
10. y=(3x+2)(x-1)+5
    1. Equation of the line of symmetry?
       
       
    2. Coordinates of the vertex?
       

Quadratic Applications

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Quadratic Discriminant

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