Quadratic Formula
Find the roots of the quadratic equation \(2x^2 - 5x + 2 = 0\)
Solving by Factoring
Solve the quadratic equation \(3x^2 - 5x - 2 = 0\) by factoring.
Solve by Completing the Square
Solve the quadratic equation \(2x^2 - 6x - 8 = 0\) by completing the square.
Finding the Perfect Square Trinomial
Find the perfect square trinomial for the quadratic equation \(y = x^2 + 4x + c\), and determine the value of \(c\).
Finding the Quadratic Equation Given the Solution Set
Find the quadratic equation whose solutions are \(2\) and \(-3\).
Finding a,b, and c in the Standard Form
NASA launches a rocket at $t=0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t)=-4.9 t^{2}+310 t+157$.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after seconds.
How high above sea-level does the rocket get at its peak?
The rocket peaks at meters above sea-level.
Finding the Discriminant
Consider the quadratic equation \(x^2 - 6x + 5 = 0\). Find the discriminant of the quadratic equation.
Finding the Quadratic Constant of Variation
Given the quadratic equation \(x^2 + 5x + k = 0\) where \(k\) is the constant of variation. The two roots of the equation are 1 and 4. Find the value of \(k\).