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alexandr402 [8]
4 years ago
15

Identify the intervals on which each quadratic function is positive. Part 2

Mathematics
1 answer:
Jet001 [13]4 years ago
6 0

Answer:  4) (-2, 6)

               5) (-∞, -3) U (-3, ∞)

               6) (-∞, -1) U (8/5, ∞)

<u>Step-by-step explanation:</u>

Find the zeros.

When the a-value is positive, the curve will be positive to the left of the leftmost zero and to the right of the rightmost zero.                   +   -   +

                                                                                                     ←---|----|--→

When the a-value is negative, the curve will be positive between the zeros.                            

                                                                                                        -   +   -

                                                                                                     ←---|----|--→

4) y = -x² + 4x + 12

  y = -(x² - 4x - 12)

  y = -(x + 2)(x - 6)

  0 = -(x + 2)(x - 6)

  0 = x + 2       0 = x - 6             --         +           --

  x = -2             x = 6              ←------|-----------|--------→

                                                     -2            6

Positive Interval: (-2, 6)    

5) y = 2x² + 12x + 18

    y = 2(x² + 6x + 9)

    y = 2(x + 3)(x + 3)

   0 = 2(x + 3)(x + 3)

   0 = x + 3       0 = x + 3               +           +

   x = -3             x = -3               ←---------|----------→

                                                            -3            

Positive Interval: (-∞, -3) U (-3, ∞)    

6) y = 5x² - 3x - 8

   y = 5x² + 5x - 8x - 8

   y = 5x(x + 1) - 8(x + 1)

   y = (5x - 8)(x + 1)

   0 = (5x - 8)(x + 1)

   0 = 5x - 8       0 = x + 1              +         --            +

   x = 8/5            x = -1               ←------|-----------|--------→

                                                         -1           8/5

Positive Interval: (-∞, -1) U (8/5, ∞)    

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An equation is formed when two equal expressions. The cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

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Step-by-step explanation:

A = 755y/t²

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