Completing the Square (Part 3)

ID: madub-sogiv
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
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45 questions

Completing the Square (Part 3)

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Problem 1

1) Select all\textbf{all} expressions that are perfect squares. Write each corresponding letter in the answer box and separate letters with commas.

a) 9x2+24x+169x^{2} + 24x + 16 \quad \quad b) 2x2+20x+1002x^{2} + 20x + 100 \quad \quad c) (73x)2(7 - 3x)^{2} \quad \quad\quad d) (5x+4)(5x4)(5x + 4)(5x - 4) \quad \quad e) (12x)(2x+1)(1 - 2x)(-2x + 1) \quad \quad\quad f) 4x2+6x+944x^{2} + 6x + \frac{9}{4} \quad \quad

Problem 2

Find the missing number that makes the expression a perfect square. Next, write the expression in factored form.

2) 49x2x+1649x^{2} - \underline{\quad}x + 16

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3) Write the expression in factored form.

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4) 36x2+x+436x^{2} + \underline{\quad}x + 4

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5) Write the expression in factored form.

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6) 4x2x+254x^{2} - \underline{\quad}x + 25

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7) Write the expression in factored form.

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8) 9x2+x+99x^{2} + \underline{\quad}x + 9

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9) Write the expression in factored form.

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10) 121x2+x+9121x^{2} + \underline{\quad}x + 9

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11) Write the expression in factored form.

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Problem 3

Find the missing number that makes the expression a perfect square. Next, write the expression in factored form.

12) 9x2+42x+9x^{2} + 42x + \underline{\quad}

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13) Write the expression in factored form.

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14) 49x228x+49x^{2} - 28x +\underline{\quad}

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15) Write the expression in factored form.

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16) 25x2+110x+25x^{2} + 110x + \underline{\quad}

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17) Write the expression in factored form.

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18) 64x2144x+64x^{2} - 144x + \underline{\quad}

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19) Write the expression in factored form.

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20) 4x2+24x+4x^{2} + 24x + \underline{\quad}

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21) Write the expression in factored form.

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Problem 4

Find the value of cc to make the expression a perfect square. Then, write an equivalent expression in factored form.

22) Find the value of cc to make 4x2 + 4x4x^2 \ + \ 4x a perfect square (ax2 + bx + c)\left(ax^2 \ + \ bx \ + \ c\right).

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23) Write an equivalent expression in factored form (kx + m)2(kx \ + \ m)^2

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24) Find the value of cc to make 25x2  30x25x^2 \ - \ 30x a perfect square (ax2 + bx + c)\left(ax^2 \ + \ bx \ + \ c\right).

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25) Write an equivalent expression in factored form (kx + m)2(kx \ + \ m)^2

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Solve each equation by completing the square.

26) 4x2+4x=34x^{2} + 4x = 3

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27) 25x230x+8=025x^{2} - 30x + 8 = 0

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Problem 5

For each function f, decide if the equation f(x)=0 has 0, 1, or 2 solutions. Explain how you know.

28) For this function ff, decide if the equation f(x)=0f(x) = 0 has 0, 1, or 2 solutions.

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29) Explain how you know.

30) For this function ff, decide if the equation f(x)=0f(x) = 0 has 0, 1, or 2 solutions.

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31) Explain how you know.

32) For this function ff, decide if the equation f(x)=0f(x) = 0 has 0, 1, or 2 solutions.

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33) Explain how you know.

34) For this function ff, decide if the equation f(x)=0f(x) = 0 has 0, 1, or 2 solutions.

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35) Explain how you know.

36) For this function ff, decide if the equation f(x)=0f(x) = 0 has 0, 1, or 2 solutions.

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37) Explain how you know.

38) For this function ff, decide if the equation f(x)=0f(x) = 0 has 0, 1, or 2 solutions.

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39) Explain how you know.

Problem 6

Solve each equation.

40) p2+10=7pp^{2} + 10 = 7p

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41) x2+11x+27=3x^{2} + 11x + 27 = 3

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42) (y+2)(y+6)=3(y + 2)(y + 6) = -3

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Problem 7

43) Which function could represent the height in meters of an object thrown upwards from a height of 25 meters above the ground t seconds after being launched?

a)

ff(tt)=-5t2t^{2}

b)

ff(tt)=-5t2t^{2}+25

c)

ff(tt)=-5t2t^{2}+25tt+50

d)

ff(tt)=-5t2t^{2}+50tt+25

Problem 8

A group of children are guessing the number of pebbles in a glass jar. The guesses and the guessing errors are plotted on a coordinate plane.

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44) Which guess is furthest away from the actual number?

45) How far is the furthest guess away from the actual number?