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 \((kx+m)^2\)
   \(4x^2+4x +\underline{\hspace{.5in}}\)
   \(25x^2-30x +\underline{\hspace{.5in}}\)

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.

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?

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.

horizontal axis, guess. scale 0 to 32, by 4's. vertical axis, absolute guessing error. scale 0 to 12, by 2's. Points plotted at 14 comma 5, 15 comma 4, 19 comma 0, 21 comma 2, 23 comma 4, 24 comma 5, 26 comma 7, 28 comma 9. 

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