- Solve the quadratic equation \(x^2 + 6x + 9 = 0\).
- Factorize and solve \(2x^2 - 4x - 6 = 0\).
- Complete the square for the quadratic expression \(x^2 + 4x + 7\).
(x+2)^2+3
- Use the completed square form to find the minimum value of the function \(f(x) = x^2 - 6x + 5\).
- Solve the quadratic equation \(3x^2 - 2x - 8 = 0\) using the quadratic formula.
- Find the roots of the equation \(4x^2 + 12x + 9 = 0\) using the quadratic formula.
- Solve the system of equations:
y = 2x + 3
y = x^2 + x - 1
- Solve the simultaneous equations:
2x + y = 4
x^2 - y = 1
- Solve the equation \(x^4 - 5x^2 + 6 = 0\).
- Find the roots of the polynomial \(x^3 - 3x^2 - 4x + 12 = 0\) by reducing it to a quadratic equation.
- Find the maximum or minimum value of \(f(x) = -2x^2 + 4x - 1\).
- Determine the vertex of the parabola \(y = x^2 - 8x + 16\).
- Solve the inequality \(x^2 - 4x + 3 < 0\).
- Determine the range of values for \(x\) such that \(2x^2 - 5x + 2 \leq 0\).
- Determine the number of real roots of the equation \(x^2 + 4x + 4 = 0\) using the discriminant.
- Find the discriminant of \(3x^2 - 2x + 5 = 0\) and determine the nature of the roots.
- Find the points of intersection between the line \(y = x + 1\) and the parabola \(y = x^2 + x\).
- Determine if the line \(y = 2x + 3\) intersects the curve \(y = x^2 - 4x + 4\).