Lesson 14

Select all expressions that are perfect squares.

\(9x^2 + 24x + 16\)

\(2x^2 + 20x + 100\)

\((7 - 3x)^2\)

\((5x + 4)(5x - 4)\)

\((1 - 2x)(\text- 2x + 1)\)

\(4x^2 + 6x + \frac94\)

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

1. \(49x^2 - \underline{\hspace{.5in}} x + 16\)
2. \(36x^2 + \underline{\hspace{.5in}} x + 4\)
3. \(4x^2 - \underline{\hspace{.5in}} x + 25\)
4. \(9x^2 + \underline{\hspace{.5in}} x + 9\)
5. \(121x^2 + \underline{\hspace{.5in}} x + 9\)

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

1. \(9x^2 + 42x + \underline{\hspace{.5in}}\)
2. \(49x^2 - 28x +\underline{\hspace{.5in}}\)
3. \(25x^2 + 110x + \underline{\hspace{.5in}}\)
4. \(64x^2 - 144x +\underline{\hspace{.5in}}\)
5. \(4x^2 + 24x + \underline{\hspace{.5in}}\)

1. 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 \((kx+m)^2\)
   \(4x^2+4x\)
   \(25x^2-30x\)

2. Solve each equation by completing the square.

   \(4x^2+4x=3\)

   \(25x^2-30x+8=0\)

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

Solve each equation.

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?

\(f(t)=\text-5t^2\)

\(f(t)=\text-5t^2+25\)

\(f(t)=\text-5t^2+25t+50\)

\(f(t)=\text-5t^2+50t+25\)

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.

1. Which guess is furthest away from the actual number?
2. How far is the furthest guess away from the actual number?