Find the Equation of the Quadratic

Here you will find a concise collection of quadratic functions practice problems of the type “find the equation of the quadratic”. Visit this page directly by visiting hunkim.com/findQuadratic

Find the Equation of the Quadratic

1. Equation of the quadratic below?
   
   
2. Equation of the quadratic below?
   
   
3. Equation of the quadratic below?
   
   
4. Equation of the quadratic below?
   
   
5. The graph below has the equation y=ax^2+6x+c. Find the values of c and a.
   
   
6. What is the equation of a parabola that has a vertex of (1,2) and has a y-intercept of 4?
7. What is the equation of a parabola that has a vertex of (2,1) and contains the point \left(4,-\frac{1}{3}\right)
8. A quadratic function passes through the points (-2,0) and (1,0). It also contains the point (0,-6). Find the equation of the quadratic in standard form: y=ax^2+bx+c.
9. The graph below is y=ax^2+bx+c. Find the values of a, b, and c.
   
10. See graph below y=ax^2+bx+c:
    
    Which of the following are positive, negative, or zero?
    1. a
    2. c
    3. b^2-4ac
    4. b
11. Let \alpha and \beta denote the roots of the quadratic equation x^2-kx+(k-1)=0.
    1. Express \alpha and \beta in terms of k.
    2. Given that \alpha^2+\beta^2=5, find the possible values of k.
       
12. What is the equation of the quadratic below?
    
13. What is the equation of the quadratic below?