Investigating Quadratics

modeling quadratics Stephany is 6 years older than Ryan. Their ages multiplied together equal 91. How old is Stephany?

• 7

• 10

• 12

• 13

solving quadratics If the quadratic formula is used to find the roots of the equation x^{2 -} 6x - 19 = 0, the correct roots are

• 1) 3 ± 2√7

• 2) -3 ± 2√7

• 3) 3 ± 4√14

• 4) -3 ± 4√14

solving quadratics: A student is asked to solve the equation 4(3x - 1)² - 17 = 83. The student's solution to the problem starts as

4(3x - 1)² = 100 A correct next

(3x - 1)² = 25 step in the solution of the problem is

• 1) 3x - 1 = ±5

• 2) 3x - 1 = ±25

• 3) 9x² - 1 = 25

• 4) 9x² - 6x + 1 = 5

Solution quadratics: What are the solutions to the equation 3(x - 4)² = 27?

• 1) 1 and 7

• 2) -1 and -7

• 3) 4 ± √24

• 4) -4 ± √24

Using the discriminant: Which equation has rational roots?

• 1) x² + 8x − 8 = 0

• 2) x² + 8x + 9 = 0

• 3) 2x² + 4x + 5 = 0

• 4) 3x²+ 8x + 4 = 0

Using the discriminant: How many real-number solutions does 4x² + 2x + 5 = 0 have?

• 1) one

• 2) two

• 3) zero

• 4) infinitely many

Using the discriminant: If the roots of a quadratic equation are real, irrational, and unequal, the discriminant could have a value of

• 1) 1

• 2) 0

• 3) 8

• 4) −6

Modeling quadratics: When Albert flips open his mathematics textbook, he notices that the product of the page numbers of the two facing pages that he sees is 156. Which equation could be used to find the page numbers that Albert is looking at?

• 1) x + (x + 1) = 156

• 2) (x + 1) + (x + 2) = 156

• 3) (x + 1)(x + 3) = 156

• 4) x(x + 1) = 156

Modeling quadratics: Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy’s age, j, if he is the younger man?

• 1) j² + 2 = 783

• 2) j² - 2 = 783

• 3) j² + 2j = 783

• 4) j² - 2j = 783

graphing quadratics: The roots of a quadratic equation can be found using the graph above

What are the roots of this equation?

• 1) −4, only

• 2) −4 and −1

• 3) −1 and 4

• 4) −4,−1, and 4