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In this lesson, we will learn how to complete the square for expressions where the coefficient of the leading term is one or otherwise.

Q1:

Given that π₯ β 1 0 π₯ = ( π₯ + π ) + π 2 2 , what are the values of π and π ?

Q2:

Given that π₯ + 2 π₯ + 5 = ( π₯ + π ) + π 2 2 , what are the values of π and π ?

Q3:

Given that 3 π₯ + 3 π₯ + 5 = π ( π₯ + π ) + π 2 2 , what are the values of π , π , and π ?

Q4:

What is the vertex form of the function π ( π₯ ) = β π₯ + 6 π₯ + 5 2 ?

Q5:

In completing the square for quadratic function π ( π₯ ) = π₯ + 1 4 π₯ + 4 6 2 , you arrive at the expression ( π₯ β π ) + π 2 . What is the value of π ?

Q6:

Given that β π₯ + 3 π₯ + 4 = π ( π₯ + π ) + π 2 2 , what are the values of π , π , and π ?

Q7:

What is the vertex form of the function π ( π₯ ) = 5 π₯ β π₯ + 1 2 ?

Q8:

Write the equation π₯ = 3 0 β 1 3 π₯ 2 in the form ( π₯ β π ) = π 2 .

Q9:

Write the equation 3 π₯ + π π₯ + π = 0 ο¨ in the form ( π₯ β π ) = π ο¨ .

Q10:

Write the equation π₯ + 6 π₯ β 3 = 0 2 in completed square form.

Q11:

Write the equation 1 + π₯ = π₯ 2 in the form ( π₯ β π ) = π 2 .

Q12:

Write the equation π₯ + π₯ + 1 = 0 2 in the form ( π₯ β π ) = π 2 .

Q13:

Write the equation 3 π₯ β 1 = 0 2 in the form ( π₯ β π ) = π 2 .

Q14:

Write the equation π₯ β π₯ = 3 4 2 in the form ( π₯ β π ) = π 2 .

Q15:

Write the equation π₯ β 2 β 3 π₯ + 1 = 0 2 in the form ( π₯ β π ) = π 2 .

Q16:

Write the equation 3 π₯ + π π₯ β 1 = 0 2 in the form ( π₯ β π ) = π 2 .

Q17:

Write the equation π₯ + π π₯ + π = 0 2 in the form ( π₯ β π ) = π 2 .

Q18:

Write the equation π π₯ + π π₯ + π = 0 ο¨ , where π β 0 , in the form ( π₯ β π ) = π ο¨ .

Q19:

Which of the following equations can be transformed into the equation 2 π₯ + 2 8 π₯ + 6 = 0 2 by expanding, rearranging, and multiplying by a scalar?

Q20:

Given that π₯ β π₯ β π = 0 2 can be written in the form ( π₯ β π ) = 3 2 , find the value of π .

Q21:

Find the values of π for which the equation π₯ + 2 π π₯ + π + π = π ο¨ ο¨ ο© is satisfied by only one value of π₯ .

Q22:

Given that ( 3 π₯ β 2 π¦ ) = 6 2 and 9 π₯ + 4 π¦ = 6 2 2 , find the value of π₯ π¦ .

Q23:

Which of the following equations can be expanded and rearranged to π₯ + 1 = 8 π₯ 2 ?

Q24:

By writing π₯ + 2 π π₯ + π = 0 2 in the form ( π₯ β π ) = π 2 , determine when the equation has no real roots.

Q25:

Factorise fully 2 4 π₯ π¦ + 3 π₯ + 4 8 π¦ 2 4 2 .

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