Exam 11: Quadratic Equations and Functions

Solve. -A ball is thrown downward with an initial velocity of 35 meters per second from a cliff that is 50 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } - 35 t + 50$ where $\mathrm { h }$ is in meters and $\mathrm { t }$ is the time in seconds since the ball was thrown. Find the time it takes the ball to hit the ground. Round your answer to the nearest tenth of a second.

Use the square root property to solve the equation. - $( 3 x - 1 ) ^ { 2 } = \frac { 4 } { 9 }$

Use the quadratic formula to solve the equation. - $( x - 2 ) ( 2 x + 1 ) = 2 ( x - 1 ) - 2$

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex. - $f ( x ) = - 3 x ^ { 2 } ; ( - 4 , - 7 )$

Solve. - $x ^ { 4 } - 22 x ^ { 2 } - 75 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( x + 2 ) ( x - 4 ) ( x - 7 ) > 0$

Use the quadratic formula to solve the equation. - $x ( 2 x + 5 ) = 2$

Solve. -Use the formula $A = P ( 1 + r ) ^ { t }$ . Find the rate, $r$ , at which $\$ 600$ grows to $\$ 739$ in 2 years.

Solve. - $x = \sqrt { 4 x + 21 }$

Match the function with its graph. - $f ( x ) = - x ^ { 2 } + 6 x$

Solve. -An express train travels 398 miles between two cities. During the first 80 miles of a trip, the train traveled through mountainous terrain. The train traveled 13 miles per hour slower through Mountainous terrain than through level terrain. If the total time to travel between the cities was 8 Hours, find the speed of the train on level terrain.

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ( x + 6 ) ( x - 2 ) > 0$

Find two possible missing terms so that the expression is a perfect square trinomial. - $x ^ { 2 } + \ldots + \frac { 9 } { 4 }$

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } + 6 x +$ ________

Use the square root property to solve the equation. - $7 x ^ { 2 } = 100$

Fill in the blank with one of the words or phrases listed below. quadratic formula quadratic discriminant \pm completing the square quadratic inequality (h,k) (0,k) (h,0) -The graph of $( x - h ) ^ { 2 } + k$ has vertex______

Find the maximum or minimum value of the function. Approximate to two decimal places. - $f ( x ) = 1.4 x ^ { 2 } - 1.2 x - 0.9$

Fill in the blank with one of the words or phrases listed below. quadratic formula quadratic discriminant \pm completing the square quadratic inequality (h,k) (0,k) (h,0) -If $a ^ { 2 } = b$ , then $a =$ _________

Solve. - $\sqrt { 22 x - 55 } = x + 3$

Find all numbers that satisfy the following. -An arrow is fired straight up from the ground with an initial velocity of 128 feet per second. Its height, $\mathrm { s } ( \mathrm { t } )$ , in feet at any time $\mathrm { t }$ is given by the function $\mathrm { s } ( \mathrm { t } ) = - 16 \mathrm { t } ^ { 2 } + 128 \mathrm { t }$ . Find the interval of time for which the height of the arrow is greater than 156 feet.