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Express -2x^2 - 12x + 7 in the form a(x + b)^2 + c. - Scottish Highers Maths - Question 12 - 2023

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Question 12

Express----2x^2---12x-+-7-in-the-form-a(x-+-b)^2-+-c.-Scottish Highers Maths-Question 12-2023.png

Express -2x^2 - 12x + 7 in the form a(x + b)^2 + c.

Worked Solution & Example Answer:Express -2x^2 - 12x + 7 in the form a(x + b)^2 + c. - Scottish Highers Maths - Question 12 - 2023

Step 1

Identify common factor

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Answer

The expression is

-2(x^2 + 6x) + 7.

We can factor out -2 from the first two terms.

Step 2

Complete the square

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Answer

Next, we complete the square for the expression inside the parentheses:

  1. Take half of 6, which is 3, and square it to get 9.
  2. This gives us:

-2(x^2 + 6x + 9 - 9) + 7 = -2((x + 3)^2 - 9) + 7.

Step 3

Process for c and write in required form

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Answer

Now we simplify:

-2((x + 3)^2 - 9) + 7 = -2(x + 3)^2 + 18 + 7 = -2(x + 3)^2 + 25.

Thus, in the form a(x + b)^2 + c, we have:

a = -2, b = 3, c = 25.

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