Mock Examination in Math 8
Quadratic Equations, Functions, and Inequalities

1. Solve each equation:
a. x 2 = 81
b. x 2 – 144 = 0
c. 6x 2 – 216 = 0
2. Transform this equation 9x 2 = 2x + 1 into standard form. Then, identify the values of a, b, and c.
3. Solve this quadratic equation using the square root property 4(x+2) 2 = 16
4. Solve this quadratic equation by factoring (x+4) (x-2) = 4x
5. Solve this quadratic equation by completing the square 3x 2 = 12x
6. Solve this equation using the quadratic formula 3(x 2 -3) = 35x+19
7. Find the quadratic equation with integral coefficients whose roots are ½ and -3/5.
8. A polygon has 27 diagonals. How many sides does it have? [Hint: The number of diagonals d of a
polygon of n sides is given by, d=n(n-3)/2.
9. By inspection, determine the sum and the product of the roots of this equation x 2 +12x+20=0
10. Without solving the equation, determine the nature of its toots 24x 2 =2x+15
11. Determine the value of k 2kx 2 -4x+k=0
12. Write a quadratic equation in standard form whose solution set is {4,4}.
13. Identify the values of a, b, and c in this quadratic equation 2x 2 +mx 2 +4=6x+2mx.
14. Solve for x, 3x 2 +2mx=m 2
15. The tens digit of a certain number is 7 less than the unit’s digit. The sum of the squares of the
two digits is 85. Find the number.
16. Transform this function y=x 2 +6x+2 into vertex form. Then, determine the value of h and k.
17. Transform this function y=5(x+3) 2 -1 into standard form. Then, identify the values of a, b, and c.
18. Use the method of completing the square to find the vertex, the axis of symmetry, and the
range of this quadratic function y=4x 2 -5x-6. Then, draw its graph.
19. Find the zeroes of the given quadratic function f(x)=2x 2 +3x-5 by factoring.
20. Find the zeroes of the given quadratic function h(x)=2x 2 -3x-5 by using the method of completing
the square.
21. Find the zeroes of the given quadratic function g(x)=x 2 -8 by using the quadratic formula.
22. Solve this quadratic inequality x 2 -3x-18≤0 using the Case Exploration Method.
23. Solve this quadratic inequality 6x 2 ≤4-5x using the Inspection-of-Signs Method.
24. Solve this quadratic inequality 12x-4≥9x 2 using the Parabola Method.