Express $-3x^2 - 6x + 7$ in the form $a(x+b)^2 + c$. - Scottish Highers Maths - Question 4 - 2018
Question 4
Express $-3x^2 - 6x + 7$ in the form $a(x+b)^2 + c$.
Worked Solution & Example Answer:Express $-3x^2 - 6x + 7$ in the form $a(x+b)^2 + c$. - Scottish Highers Maths - Question 4 - 2018
Step 1
Identify common factor
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Answer
First, we can factor out −3 from the first two terms:
−3(x2+2x)+7
Step 2
Complete the square
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Answer
Next, we complete the square for the expression inside the parentheses:
x2+2x=(x+1)2−1
Thus, we can rewrite the equation as:
−3((x+1)2−1)+7
Step 3
Process for $c$
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Answer
Distributing −3 gives us:
−3(x+1)2+3+7
Now, simplify:
−3(x+1)2+10
Therefore, we have expressed the original quadratic in the desired form as:
a=−3,b=1,c=10
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