Practice solving quadratic equations by factoring, using square roots, and applying the quadratic formula. Students also identify key features such as roots and vertex form.
Read each problem carefully. Solve each quadratic equation or answer the question. Show your work and write your answers in complete mathematical statements.
Solving and analyzing quadratic equations
Math - Grade 9-12
- 1
Solve the equation x^2 - 9 = 0.
- 2
Solve the equation x^2 + 5x + 6 = 0 by factoring.
- 3
Solve the equation x^2 - 7x + 12 = 0 by factoring.
- 4
Solve the equation 2x^2 - 8 = 0.
- 5
Solve the equation x^2 + 2x - 8 = 0 by factoring.
- 6
Solve the equation x^2 - 6x + 5 = 0 by factoring.
- 7
Solve the equation x^2 + 4x + 1 = 0 using the quadratic formula.
- 8
Solve the equation 3x^2 - 12x = 0 by factoring.
- 9
Solve the equation x^2 = 16.
- 10
Write the equation x^2 - 4x - 12 = 0 in factored form and then solve it.
- 11
For the quadratic y = x^2 - 6x + 8, find the x-intercepts by solving x^2 - 6x + 8 = 0.
- 12
Find the vertex of y = x^2 - 4x + 7.
- 13
Solve the equation x^2 + 10x + 25 = 0.
- 14
Determine the number of real solutions for the equation x^2 + 2x + 5 = 0.
- 15
A ball is launched upward and its height is modeled by h = -16t^2 + 48t. Find the times when the ball is on the ground.