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Factored Form of Quadratic Equations - Understanding, Roots, and Factors

Learn to write quadratic equations in factored form with given roots, factors, and points on the parabola. Discover the concepts of single, double, or twin roots and how many parabolas share the same roots.

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Factored Form of Quadratic Equations - Understanding, Roots, and Factors

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  1. Which of the following gives enough information to write an equation in factored form? • “a” and two roots • Two roots and a third point • The x-intercepts and “a” • All of the above • How many parabolas can contain the same roots? • One • Two—one opening upwards and one opening downwards • An infinite number

  2. Factored Form of a Quadratic Equation • This parabola has one root. What is this called? • Single root • Twin root • Double root • Shadow root

  3. Factored Form of a Quadratic Equation • What are the roots of the parabola? • x = 1 and x = 5 • x = -1 and x = 5 • x = -5 and x = -1 • x = -5 and x = 1

  4. Factored Form of a Quadratic Equation • What are the factors of the equation for the parabola? • (x  4) and (x  8) • (x + 4) and (x + 8) • (x  4) and (x + 8) • (x + 4) and (x  8)

  5. Factored Form of a Quadratic Equation • What are the factors of the equation for the parabola? • (x  1) and (x 3) • (x + 1) and (x + 3) • (x  1) and (x + 3) • (x + 1) and (x 3)

  6. Factored Form of a Quadratic Equation • Which of the following is another point on the parabola? • (1, 2) • (5, 2) • (4, -3) • (-2, 3)

  7. Factored Form of a Quadratic Equation • Which is the equation of the parabola in factored form? • y = (x + 3)(x + 8) • y = (x 3)(x + 8) • y = (x + 3)(x + 3) • y = (x + 3)(x  3)

  8. Factored Form of a Quadratic Equation • Which is the equation of the parabola in factored form? • y = (x + 7)(x  6) • y = 0.1(x + 7)(x  6) • y = 3/14(x + 7)(x  6) • y = 0.5(x + 7)(x  6)

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