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elixir [45]
3 years ago
5

Will mark brainliest if answered

Mathematics
1 answer:
Delvig [45]3 years ago
4 0

Answer:

See below

Step-by-step explanation:

The vertex form of a parabola is  y = a(x - h)^2 + k

If the leading coefficient is positive, the parabola opens upward, and (h, k) represents the vertex, or turning point.

1a. The leading coefficient is 4, which is positive, meaning the parabola opens upwards. From the vertex form, we can say the vertex(turning point) is (2, 7).

1b. The leading coefficient is -3, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-6, 4).

1c. The leading coefficient is -1, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-4, -3).

To write the vertex form of a parabola, we need to complete the square. A perfect square trinomial is in the form a^2 + 2ab + b^2. In these cases we are already given a^2 and 2ab.

2a. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to 6x. From this, we can say a = x. Now, we can plug that in:

2ab = 6x

2(x)b = 6x

b = 3

Therefore, the last term b^2, is 3^2 or 9. We can add 9 and subtract nine to keep the equation equivalent:

y = x^2 + 6x + 9 - 9 - 2

Now, we can factor the square into (a + b)^2 and simplify:

y = (x + 3)^2 - 11

From this form, the vertex(turning point) will be (-3, -11). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.

2b. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to -2x. From this, we can say a = x. Now, we can plug that in:

2ab = -2x

2(x)b = -2x

b = -1

Therefore, the last term b^2, is (-1)^2 or 1. We can add 1 and subtract nine to keep the equation equivalent:

y = x^2 - 2x + 1 - 1 + 11

Now, we can factor the square into (a + b)^2 and simplify:

y = (x - 1)^2 + 10

From this form, the vertex(turning point) will be (1, 10). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

<h3>Solving linear equation with one variable:</h3>

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        Add 4 to both sides

      -4 + 3x + 4 = 4x - 8 +  4

               3x     = 4x - 4

Subtract 4x from both sides,

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              -x   = -4

                \sf \boxed{\bf x = 4}

2) -5x - 8 = 2

Add 8 to both sides

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Divide both sides by (-5)

            \sf \dfrac{-5}{-5}x =\dfrac{10}{-5}

                 \sf \boxed{\bf x = -2}

3) 12r - 14 = 5(2-r)

    12r - 14 = 5*2 - 5*r

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Add 14 to both sides

 12r - 14 + 14 = 10 - 5r + 14

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Add 5r to both sides

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Divide both sides by 17

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4) 3x - 8 = -(17 + 2x)

  3x - 8 = -17 - 2x

Add 8 to both sides

3x - 8 + 8 = -17 - 2x + 8

           3x = -9 - 2x

Add 2x to both sides

      3x + 2x = -9

            5x  = -9

Divide both sides by 5

              \sf \dfrac{5}{5}x=\dfrac{-9}{5}\\\\\boxed{x = \dfrac{-9}{5}}

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2 years ago
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Answer:

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Step-by-step explanation:

We can use the order of operations (PEMDAS), to solve this equation.

We must first multiply and divide, and order. This means we divide 12 by 3 and get 4, then multiply that by 2 and get 8. (30-12÷3×2,30-4×2,30-8). Now we just subtract 8 from 30 and get 22 as our answer.

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