Quadratic Equations

Quadratic equations are essentially second-degree polynomials that consist of three different coefficients. They are typically written in the format of ax² + bx + c = 0. The methods employed for finding solutions include factorization, the quadratic formula, or the technique of completing the square. The graph of a quadratic equation takes the shape of a parabola, with the vertex and axis of symmetry being calculable.

Quadratic Formula

Find the roots of the quadratic equation 2x25x+2=0

Solving by Factoring

Solve the quadratic equation 3x25x2=0 by factoring.

Solve by Completing the Square

Solve the quadratic equation 2x26x8=0 by completing the square.

Finding the Perfect Square Trinomial

Find the perfect square trinomial for the quadratic equation y=x2+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)=4.9t2+310t+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 x26x+5=0. Find the discriminant of the quadratic equation.

Finding the Quadratic Constant of Variation

Given the quadratic equation x2+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.