Unit 8 Quadratic Equations Homework 2 Graphing Quadratic Equations (2024)

FAQs

Do quadratic equations have 2 answers? ›

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.

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, (b [ 2 ] - 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

Answer: The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x^2 + 3x + 1.

The quadratic equation of the standard form ax2+bx+c has two solutions. The solutions or roots of quadratic equations can be positive/negative, same/distinct, and real or imaginary.

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.

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) .

Read below for an explanation of the three main forms of quadratics (standard form, factored form, and vertex form), examples of each form, as well as strategies for converting between the various quadratic forms. Your mathematics journey has taken you far.

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.

Step 1: Using inverse operations, move all terms to one side of your equal sign. Step 2: Simplify your equation, and move terms around so that your equation is in the standard form of a quadratic function. Step 3: Now that your equation is in standard form, you can determine the values for a, b, and c.

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.

Can a system of equations have 2 answers? ›

Number of Solutions

Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.)

The solution of a quadratic equation ax² + bx + c = 0 is given by the quadratic formula x = [-b ± √(b² - 4ac)] / 2a, to find the solution of a quadratic equation. In the case of one real solution, the value of discriminant b² - 4ac is zero. For example, x² + 2x + 1 = 0 has only one solution x = -1.

False, because some quadratic equations involve the product of the GCF and two binomials, so those may have three solutions.