Exam 9: Quadratic Equations

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Give the correct final term for the following expression to ensure that the resulting trinomial is a perfect square trinomial. Give the correct final term for the following expression to ensure that the resulting trinomial is a perfect square trinomial.

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If If   what are   and   ?   __________   __________ what are If   what are   and   ?   __________   __________ and If   what are   and   ?   __________   __________ ? If   what are   and   ?   __________   __________ __________ If   what are   and   ?   __________   __________ __________

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Solve the quadratic equation. Use whatever method seems to fit the situation or is convenient for you. Solve the quadratic equation. Use whatever method seems to fit the situation or is convenient for you.

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The lengths of all three sides of an equilateral triangle are 18 feet. Find the height of the triangle.

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Multiply the complex numbers. Multiply the complex numbers.

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Graph the equation. Begin by completing the square on the first two terms. Graph the equation. Begin by completing the square on the first two terms.

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Solve the quadratic equation. Use whatever method seems to fit the situation or is convenient for you. Solve the quadratic equation. Use whatever method seems to fit the situation or is convenient for you.

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Solve the quadratic equation. Use whatever method seems to fit the situation or is convenient for you. Solve the quadratic equation. Use whatever method seems to fit the situation or is convenient for you.

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At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet)of the coin tossed in the air is At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet)of the coin tossed in the air is   . To find the times at which the coin is   feet above the ground we substitute   for h in the equation, giving us   . Solve this equation for t to find the times at which the coin is   feet above the ground.   t = __________ seconds . To find the times at which the coin is At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet)of the coin tossed in the air is   . To find the times at which the coin is   feet above the ground we substitute   for h in the equation, giving us   . Solve this equation for t to find the times at which the coin is   feet above the ground.   t = __________ seconds feet above the ground we substitute At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet)of the coin tossed in the air is   . To find the times at which the coin is   feet above the ground we substitute   for h in the equation, giving us   . Solve this equation for t to find the times at which the coin is   feet above the ground.   t = __________ seconds for h in the equation, giving us At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet)of the coin tossed in the air is   . To find the times at which the coin is   feet above the ground we substitute   for h in the equation, giving us   . Solve this equation for t to find the times at which the coin is   feet above the ground.   t = __________ seconds . Solve this equation for t to find the times at which the coin is At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet)of the coin tossed in the air is   . To find the times at which the coin is   feet above the ground we substitute   for h in the equation, giving us   . Solve this equation for t to find the times at which the coin is   feet above the ground.   t = __________ seconds feet above the ground. At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet)of the coin tossed in the air is   . To find the times at which the coin is   feet above the ground we substitute   for h in the equation, giving us   . Solve this equation for t to find the times at which the coin is   feet above the ground.   t = __________ seconds t = __________ seconds

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Combine the complex numbers. Combine the complex numbers.

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Solve the equation by completing the square. Solve the equation by completing the square.

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Solve the equation by completing the square. Solve the equation by completing the square.

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If a comet approaches the sun with exactly the right velocity and direction, its orbit around the sun will be a parabola. (Such a comet only will be seen once and then will leave the solar system forever.)A certain comet s orbit is given by If a comet approaches the sun with exactly the right velocity and direction, its orbit around the sun will be a parabola. (Such a comet only will be seen once and then will leave the solar system forever.)A certain comet s orbit is given by   where both   and   are measured in millions of miles, and the sun s position is at the origin   Graph the comet s orbit between   and   How far is the comet from the sun when the comet crosses the x -axis? where both If a comet approaches the sun with exactly the right velocity and direction, its orbit around the sun will be a parabola. (Such a comet only will be seen once and then will leave the solar system forever.)A certain comet s orbit is given by   where both   and   are measured in millions of miles, and the sun s position is at the origin   Graph the comet s orbit between   and   How far is the comet from the sun when the comet crosses the x -axis? and If a comet approaches the sun with exactly the right velocity and direction, its orbit around the sun will be a parabola. (Such a comet only will be seen once and then will leave the solar system forever.)A certain comet s orbit is given by   where both   and   are measured in millions of miles, and the sun s position is at the origin   Graph the comet s orbit between   and   How far is the comet from the sun when the comet crosses the x -axis? are measured in millions of miles, and the sun s position is at the origin If a comet approaches the sun with exactly the right velocity and direction, its orbit around the sun will be a parabola. (Such a comet only will be seen once and then will leave the solar system forever.)A certain comet s orbit is given by   where both   and   are measured in millions of miles, and the sun s position is at the origin   Graph the comet s orbit between   and   How far is the comet from the sun when the comet crosses the x -axis? Graph the comet s orbit between If a comet approaches the sun with exactly the right velocity and direction, its orbit around the sun will be a parabola. (Such a comet only will be seen once and then will leave the solar system forever.)A certain comet s orbit is given by   where both   and   are measured in millions of miles, and the sun s position is at the origin   Graph the comet s orbit between   and   How far is the comet from the sun when the comet crosses the x -axis? and If a comet approaches the sun with exactly the right velocity and direction, its orbit around the sun will be a parabola. (Such a comet only will be seen once and then will leave the solar system forever.)A certain comet s orbit is given by   where both   and   are measured in millions of miles, and the sun s position is at the origin   Graph the comet s orbit between   and   How far is the comet from the sun when the comet crosses the x -axis? How far is the comet from the sun when the comet crosses the x -axis?

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An advertisement for a portable computer indicates it has a 13-inch viewing screen. This means that the diagonal of the screen measures 13 inches. If the ratio of the height to the width of the screen is 3 to 4, we can represent the height with 3 x and the width with 4 x , and then use the Pythagorean theorem to solve for x . Once we have x , the height will be 3 x and the width will be 4 x . Find the height and width of this computer screen to the nearest tenth of an inch. Width = __________ in. Height = __________ in.

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Solve the equation. Solve the equation.

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Solve the equation by using the quadratic formula. Solve the equation by using the quadratic formula.

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Solve the equation by completing the square. Solve the equation by completing the square.

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To apply the quadratic formula to the equation To apply the quadratic formula to the equation   you have to notice that   Solve the equation using the quadratic formula. you have to notice that To apply the quadratic formula to the equation   you have to notice that   Solve the equation using the quadratic formula. Solve the equation using the quadratic formula.

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Graph the equation. Graph the equation.

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Solve the equation by completing the square. Solve the equation by completing the square.

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