Steps for Solving Quadratics

What is the process of solving quadratics by factoring?

• Finding two binomials that multiply together to give the quadratic expression and setting each binomial equal to zero to solve for the variable.

• Subtracting the quadratic expression from a binomial to find the variable.

• Dividing the quadratic expression by a binomial to find the variable.

• Finding two trinomials that multiply together to give the quadratic expression and setting each trinomial equal to zero to solve for the variable.

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CCSS.HSA-REI.B.4B

How can you solve quadratics by graphing?

• Plot the points where the graph intersects the line y = 0.

• Find the x-intercepts or points where the graph intersects the x-axis.

• Use the quadratic formula to find the solutions.

• Find the y-intercepts or points where the graph intersects the y-axis.

What is the method of solving quadratics by completing the square?

• Graphing the quadratic equation

• Factoring the quadratic equation

• Manipulating the equation to create a perfect square trinomial

• Using the quadratic formula

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CCSS.HSA-REI.B.4B

What are the steps involved in factoring quadratics?

• The steps involved in factoring quadratics are: 1. Multiply the quadratic equation by a constant. 2. Divide the quadratic equation by a constant. 3. Add the constant term to both sides of the equation. 4. Subtract the constant term from both sides of the equation. 5. Rewrite the quadratic equation as the sum of two binomials.

• The steps involved in factoring quadratics are: 1. Square the quadratic equation. 2. Take the square root of the quadratic equation. 3. Add the square root of the constant term to both sides of the equation. 4. Subtract the square root of the constant term from both sides of the equation. 5. Rewrite the quadratic equation as the difference of two binomials.

• The steps involved in factoring quadratics are: 1. Write the quadratic equation in the form ax^2 + bx + c = 0. 2. Factor out the greatest common factor (if any). 3. Use the AC method or trial and error to find two numbers that multiply to give the constant term (c) and add up to give the coefficient of the linear term (b). 4. Rewrite the quadratic equation as the product of two binomials. 5. Set each binomial equal to zero and solve for x. The solutions will be the factors of the quadratic equation.

• The steps involved in factoring quadratics are: 1. Divide the quadratic equation by the coefficient of the linear term. 2. Multiply the quadratic equation by the coefficient of the linear term. 3. Add the coefficient of the linear term to both sides of the equation. 4. Subtract the coefficient of the linear term from both sides of the equation. 5. Rewrite the quadratic equation as the sum of two binomials.

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CCSS.HSA-REI.B.4B

Find the zeros of this quadratic.

• b=4/5, b=3

• b=4, b=-3

• b=1/5, b=3

• b=4/5, b=-3

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CCSS.HSA-REI.B.4B

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

• 4

• 2

• 8

• 20

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CCSS.HSA-REI.B.4B

Complete the square for

x² + 12x + ____

(find the missing number in the blank)

• x² + 12x + 144

• x² + 12x + 36

• x² + 12x - 36

• x² + +12x - 144

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CCSS.HSA-REI.B.4B

Complete the square for

x² - 14x + ____

(find the missing value that goes in the blank)

• - 196

• 49

• - 49

• 28

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CCSS.HSA-REI.B.4B

What should be added to both sides of the following equation to complete the square?
x² + 12x = 5

• 12

• 6

• 36

• 5

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CCSS.HSA-REI.B.4B

• Factors: (x +2) and (x+9)

  Solutions: x = -2, -9

• Factors: (x -6) and (x-3)

  Solutions: x = -3, -6

• Factors: (x -2) and (x-9)

  Solutions: x = 2, 9

• Factors: (x +18) and (x-1)

  Solutions: x = 1, -18

Tags

CCSS.HSA-REI.B.4B