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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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