Lesson 16

For each equation, identify the values of \(a\), \(b\), and \(c\) that you would substitute into the quadratic formula to solve the equation.

1. \(3x^2 + 8x + 4 = 0\)
2. \(2x^2 - 5x + 2 = 0\)
3. \(\text- 9x^2 + 13x - 1 = 0\)
4. \(x^2 + x - 11 = 0\)
5. \(\text- x^2 + 16x + 64 = 0\)

Use the quadratic formula to show that the given solutions are correct.

1. \(x^2 + 9x + 20 =0\). The solutions are \(x = \text- 4\) and \(x = \text- 5\).
2. \(x^2 - 10x + 21 = 0\). The solutions are \(x = 3\) and \(x = 7\).
3. \(3x^2 - 5x + 1 = 0\). The solutions are \(x = \frac56 \pm \frac{\sqrt{13}}{6}\).

Select all the equations that are equivalent to \(81x^2+180x-200=100\)

\(81x^2+180x-100=0\)

\(81x^2+180x+100=200\)

\(81x^2+180x+100=400\)

\((9x+10)^2=400\)

\((9x+10)^2=0\)

\((9x-10)^2=10\)

\((9x-10)^2=20\)

Technology required. Two objects are launched upward. Each function gives the distance from the ground in meters as a function of time, \(t\), in seconds.

Use graphing technology to graph each function.

1. Which object reaches the ground first? Explain how you know.
2. What is the maximum height of each object?

Identify the values of \(a\), \(b\), and \(c\) that you would substitute into the quadratic formula to solve the equation.

1. \(x^2 + 9x + 18 = 0\)
2. \(4x^2 - 3x + 11 = 0\)
3. \(81 - x + 5x^2 = 0\)
4. \(\frac45 x^2 + 3x = \frac13 \)
5. \(121 = x^2\)
6. \(7x + 14x^2 = 42\)