Quadratic Equations Coloring Activity Answer Key (2024)

FAQs

Are there 2 answers for the quadratic formula? ›

Solving the quadratic equation. A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.

Are you referring to the signs on the terms in a quadratic equation. In general, however, ALL quadratic equations will have two solutions. Often they are both real and might be both positive, both negative, or one positive and one negative. Sometimes one or both of the solutions will be complex (i, sqrt[-1]).

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b² - 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

Answer: There are various methods by which you can solve a quadratic equation such as: factorization, completing the square, quadratic formula, and graphing. These are the four general methods by which we can solve a quadratic equation.

Answer: If a quadratic equation has exactly one real number solution, then the value of its discriminant is always zero. A quadratic equation in variable x is of the form ax² + bx + c = 0, where a ≠ 0.

Set the equation equal to zero. If the quadratic side is factorable, factor, then set each factor equal to zero. If the quadratic equation involves a SQUARE and a CONSTANT (no first degree term), position the square on one side and the constant on the other side. Then take the square root of both sides.

Factoring is the first of the three methods of solving quadratic equations. It is often the fastest way to solve a quadratic equation, so usually should be attempted before any other method. This method relies on the fact that if two expressions multiply to zero, then at least one of them must be zero.

If b² - 4ac is positive (>0) then we have 2 solutions. If b² - 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/2a. So x = -b/2a, giving only one solution. Lastly, if b² - 4ac is less than 0 we have no solutions.

Is quadratic equation tough? ›

Quadratic equations are hard to understand for people, who lack some underlying knowledges or informations; I dare to say, only then.

Quadratic Functions Formula

The general form of a quadratic function is given as: f(x) = ax² + bx + c, where a, b, and c are real numbers with a ≠ 0. The roots of the quadratic function f(x) can be calculated using the formula of the quadratic function which is: x = [ -b ± √(b² - 4ac) ] / 2a.

The quadratic equation formula to solve the equation ax² + bx + c = 0 is x = [-b ± √(b² - 4ac)]/2a. Here we obtain the two values of x, by applying the plus and minus symbols in this formula. Hence the two possible values of x are [-b + √(b² - 4ac)]/2a, and [-b - √(b² - 4ac)]/2a.

FAQs on Discriminant Formulas

The discriminant formulas are as follows: The discriminant formula of a quadratic equation ax² + bx + c = 0 is, Δ (or) D = b² - 4ac.

The quadratic equation always has two solutions of the variables. The solutions can be negative, positive, same, or different.

All quadratic equations of the form ax^2 + bx + c have precisely two roots (solutions) and no more. The discriminant, D = (b^2 - 4ac), tells you what types of roots they are. If D is positive, then there two real roots.

Quadratic equations can have at most two solutions. The number of solutions are not fixed to 2, it can also be none, unique, or two solutions. The given statement is False. Quadratic equations are not fixed to two real solutions, there can be two, one, or no real solutions at all.