Completing the Square (Edexcel GCSE Maths): Quizzes

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Completing the Square
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What is the target form when completing the square for a quadratic expression?

(x+p)2+q(x + p)^2 + q

In Step 2, what do you do with the coefficient of xx to form the initial bracket?

Divide it by 2

What is the most common mistake when completing the square?

Forgetting the adjusting number in Step 4

For x2+8x+5x^2 + 8x + 5, what is the initial bracket formed in Step 2?

(x+4)2(x + 4)^2

What is the completed square form of x2+8x+5x^2 + 8x + 5?

(x+4)211(x + 4)^2 - 11

What value of aa in ax2+bx+cax^2 + bx + c makes completing the square more straightforward?

a=1a = 1

When solving using completed square, which operation produces the ±\pm symbol?

Taking the square root

What are the solutions to x2+8x+5=0x^2 + 8x + 5 = 0 using completing the square?

x=4±11x = -4 \pm \sqrt{11}

What is the quick formula for the adjusting number when the coefficient of x2x^2 is 1?

c(b2)2c - (\frac{b}{2})^2

When is completing the square particularly useful?

When the quadratic doesn't factorise

What is the purpose of the adjusting number in Step 4?

To make the expression equal the original

What important information does completing the square reveal about a quadratic?

Its vertex

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