Lesson 14
Completing the Square (Part 3)
- Let’s complete the square for some more complicated expressions.
Problem 1
Select all expressions that are perfect squares.
\(9x^2 + 24x + 16\)
\(2x^2 + 20x + 100\)
\((7 - 3x)^2\)
\((5x + 4)(5x - 4)\)
\((1 - 2x)(\text- 2x + 1)\)
\(4x^2 + 6x + \frac94\)
Problem 2
Find the missing number that makes the expression a perfect square. Next, write the expression in factored form.
- \(49x^2 - \underline{\hspace{.5in}} x + 16\)
- \(36x^2 + \underline{\hspace{.5in}} x + 4\)
- \(4x^2 - \underline{\hspace{.5in}} x + 25\)
- \(9x^2 + \underline{\hspace{.5in}} x + 9\)
- \(121x^2 + \underline{\hspace{.5in}} x + 9\)
Problem 3
Find the missing number that makes the expression a perfect square. Next, write the expression in factored form.
- \(9x^2 + 42x + \underline{\hspace{.5in}}\)
- \(49x^2 - 28x +\underline{\hspace{.5in}}\)
- \(25x^2 + 110x + \underline{\hspace{.5in}}\)
- \(64x^2 - 144x +\underline{\hspace{.5in}}\)
- \(4x^2 + 24x + \underline{\hspace{.5in}}\)
Problem 4
- Find the value of \(c\) to make the expression a perfect square. Then, write an equivalent expression in factored form.
standard form \(ax^2+bx+c\) factored form \((kx+m)^2\) \(4x^2+4x\) \(25x^2-30x\) -
Solve each equation by completing the square.
\(4x^2+4x=3\)
\(25x^2-30x+8=0\)
Problem 5
For each function \(f\), decide if the equation \(f(x)=0\) has 0, 1, or 2 solutions. Explain how you know.
A
B
C
D
E
F
Problem 6
Solve each equation.
\(p^2+10=7p\)
\(x^2+11x+27=3\)
\((y+2)(y+6)=\text-3\)
Problem 7
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?
\(f(t)=\text-5t^2\)
\(f(t)=\text-5t^2+25\)
\(f(t)=\text-5t^2+25t+50\)
\(f(t)=\text-5t^2+50t+25\)
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.
- Which guess is furthest away from the actual number?
- How far is the furthest guess away from the actual number?