Exam 8: Quadratic Equations and Functions

Solve. -A rocket is launched from the top of a cliff that is 48 feet high with an initial velocity of 120 feet per second. The height, $h$ , of the rocket after $t$ seconds is given by the equation $h = - 16 t ^ { 2 } + 120 t + 48$ . How long after the rocket is launched will it strike the ground? Round to the nearest tenth of a second, if necessary.

Solve the equation by completing the square. - $x ^ { 2 } + 8 x = 5$

Solve. - $x ^ { 3 } + 11 x + x ^ { 2 } + 11 = 0$

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } + \frac { 4 } { 9 } x$

Solve. - $\sqrt { 18 x + 9 } = x + 5$

Use the square root property to solve the equation. $( 2 x - 1 ) ^ { 2 } = 25$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 3 x - 10 < 0$

Solve. -A ball is thrown downward with an initial velocity of 42 meters per second from a cliff that is 100 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } - 42 t + 120$ where $h$ is in meters and $t$ is the time in seconds since the ball was thrown. Find the time that the ball will be 20 meters from the ground. Round your answer to the nearest tenth of a second.

Solve the inequality. Write the solution set in interval notation. - $( 3 x + 2 ) ( 4 x - 1 ) > 0$

Use the quadratic formula to solve the equation. - $4 x ^ { 2 } = - 10 x - 3$

Solve. -The manufacturer of a CD player has found that the revenue function for selling $\mathrm { P } C D$ players is $R ( p ) = - 5 p ^ { 2 } + 1560 p$ . Find the maximum revenue to the nearest whole dollar.

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } - 3 x ^ { 2 } - 6 x + 8 \geq 0$

Solve. -A person is standing on the top of a building 50 feet above the ground. They project an object upward with an initial velocity of 40 feet per second. The object's distance above the ground, $\mathrm { d }$ , after $t$ seconds may be found by the formula $d = - 16 t ^ { 2 } + 40 t + 50$ . What is the maximum height the object will reach. How much time does it take to fall back to the ground? Assume that it takes the same time for going up and coming down.

Solve the inequality. Write the solution set in interval notation. - $\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 16 } > 0$

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - $f ( x ) = 10 + 7 x + x ^ { 2 }$

Solve the equation by completing the square. - $x ^ { 2 } + 14 x = - 26$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = 2 x ^ { 2 }$

Solve. - $x ^ { 4 } + 16 = 17 x ^ { 2 }$

Solve. - $x ^ { 4 } - 23 x ^ { 2 } = 50$