Solving Quadratic Equations

If the equation $x^{2} - 5x + 6 = 0$ is factored, what are the roots of the equation?

A projectile is launched and its height $h$ in meters after $t$ seconds is given by the equation $h(t) = -4.9t^{2} + 20t + 1$. What is the maximum height reached?

Which of the following equations has a discriminant of zero?

A rectangular garden is designed such that its length is twice its width. If the area of the garden is $72$ square meters, what are the dimensions of the garden?

What are the solutions to the equation $3x^{2} + 12x + 12 = 0$?

If $x^{2} - kx + 15 = 0$ has roots $3$ and $5$, what is the value of ?

What is the vertex of the parabola represented by $y = x^{2} - 4x + 3$?

A quadratic function $f(x) = ax^{2} + bx + c$ has a maximum value of $10$ when . What is the value of if ?