Solving+Quadratic+Equations-Target+A-Solving+Quadratics-Guided+Learning

Solving Quadratic Equations Target A: Solve a quadratic equation. (Factoring, Completing the Square, Using Square roots, Quadratic Formula)

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Estimate the area of the patio. Explain your reasoning. || A quadratic equation is polynomial equation with a degree of two, meaning the highest valued exponent in the equation is a two. Which of the following are quadratic equations?

A) //y// = 3//x// - 2 B) 8 = -4//x// 2 + 6//x// - 7 C) //f//(//x//) = 9//x// 2 D) 7//x// - 6 = 15 E) //f//(//x//) = -|//x// - 6| + 3

The equations from B and C are quadratic equations. Each equation has a term in which the highest degree is a 2. In this target, you are learning how to solve a quadratic equation. Why would we want to know how to do this? Solving a quadratic equation reveals the "zeros" of the function. This is important for graphing a quadratic function which we will be doing in the next unit Graphing Quadratic Functions There are several methods you can use to solve a quadratic equation: factoring, using square roots, completing the square, and using the quadratic formula. Below are steps and examples on how to solve a quadratic equation for each method. To learn when to use each method, see Solving Quadratic Equations Target B Guided Learning.

1) Make sure one side of the equation is equal to zero 2) Check to see if you can factor out a GCF (if you factor out a GCF and there is no longer an //x// 2 -term, quadratic term, proceed to step 4) 3) Factor – Difference of Two Squares, Perfect Square Trinomial, or Guess and Check 4) Set each factor equal to zero by using the Zero Product Property 5) Solve each equation
 * Method 1: Factoring**


 * Solving Quadratic Equations by Factoring Quick Check**

1) -8x 2 + 20x = 0

2) 2x 2 - 21x + 25 = -15

Solving Quadratic Equations by Factoring Quick Check Solutions

1) Isolate the “squared” expression 2) Take the square root of both sides of the equation 3) Solve for the variable
 * Method 2: Using Square Roots**

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 * Solving Quadratic Equations Using Square Roots Quick Check**

1) 6x 2 - 15 = 27

2) 4(x - 2) 2 = 20

Solving Quadratic Equations Using Square Roots Quick Check Solutions

1) Isolate the //x// 2 -term and the //x-//term on one side of the equation (isolate the constant on the other side) 2) Make sure leading coefficient is 1 3) Complete the square: divide the coefficient of the x-term (linear term) by 2, square this number, and add this number to both sides of the equation to write an equivalent equation 4) Write the trinomial as a perfect square: (x ___) 2 5) Solve the equation using Square Roots
 * Method 3: Completing the Square**

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 * Solving Quadratic Equations by Completing the Square Quick Check**

1) x 2 - 14x + 3 = 15

2) 2x 2 + 16x - 8 = 0

Solving Quadratic Equations by Completing the Square Quick Check Solutions

The quadratic formula is another approach to solving a quadratic equation. Here is the quadratic formula: To help you remember the formula, you can sing the following words to the tune of "Pop Goes the Weasel":
 * Method 4: Quadratic Formula**

x equals negative b plus or minus the square root of b squared minus four a c all over two a  Listen to the song media type="youtube" key="rKI1wy4nWpo" height="100" width="150"

The quadratic formula is derived from solving the standard equation a//x// 2 + b//x// + c = 0 by completing the square. To see how the quadratic formula is derived click here.

Steps for a quadratic equation using the quadratic formula:

1) Make sure the equation is in standard form (descending order) and equal to zero 2) Identify the a, b, and c 3) Substitute a, b, and c into the quadratic formula 4) Evaluate to find the value of the variable






 * Solving Quadratic Equations Using the Quadratic Formula Quick Check**

1) x 2 - 3x - 7 = 0

2) 3x 2 -11x + 14 = 4

Solving Quadratic Equations Using the Quadratic Formula Quick Check Solutions