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Solve Applications of the Quadratic Formula

In the following exercises, solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The product of two consecutive odd numbers is 255. Find the numbers.

Two consecutive odd numbers whose product is 255 are 15 and 17, and −15 and −17 .

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The product of two consecutive even numbers is 360. Find the numbers.

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The product of two consecutive even numbers is 624. Find the numbers.

Two consecutive even numbers whose product is 624 are 24 and 26, and −26 and −24 .

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The product of two consecutive odd numbers is 1023. Find the numbers.

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The product of two consecutive odd numbers is 483. Find the numbers.

Two consecutive odd numbers whose product is 483 are 21 and 23, and −21 and −23 .

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The product of two consecutive even numbers is 528. Find the numbers.

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A triangle with area 45 square inches has a height that is two less than four times the width. Find the height and width of the triangle.

The width of the triangle is 5 inches and the height is 18 inches.

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The width of a triangle is six more than twice the height. The area of the triangle is 88 square yards. Find the height and width of the triangle.

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The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is three feet. Find the lengths of the three sides of the triangle.

The leg of the right triangle is 1.7 feet and the hypotenuse is 3.4 feet.

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The hypotenuse of a right triangle is 10 cm long. One of the triangle’s legs is three times the length of the other leg. Round to the nearest tenth. Find the lengths of the three sides of the triangle.

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A farmer plans to fence off sections of a rectangular corral. The diagonal distance from one corner of the corral to the opposite corner is five yards longer than the width of the corral. The length of the corral is three times the width. Find the length of the diagonal of the corral.

The image shows rectangle with the long sides horizontal. A diagonal line runs from the top left corner of the rectangle to the bottom right corner.

The length of the fence is 7.1 units.

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Nautical flags are used to represent letters of the alphabet. The flag for the letter O consists of a yellow right triangle and a red right triangle which are sewn together along their hypotenuse to form a square. The adjoining side of the two triangles is three inches longer than a side of the flag. Find the length of the side of the flag.

The image shows a square with a diagonal line running from the top left corner to the bottom right corner. The diagonal splits the square into two right triangles. The lower triangle is red and the upper triangle is yellow.
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The length of a rectangular driveway is five feet more than three times the width. The area is 350 square feet. Find the length and width of the driveway.

The width of the driveway is 10 feet and its length is 35 feet.

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A rectangular lawn has area 140 square yards. Its width that is six less than twice the length. What are the length and width of the lawn?

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A firework rocket is shot upward at a rate of 640 ft/sec. Use the projectile formula h = −16 t 2 + v 0 t to determine when the height of the firework rocket will be 1200 feet.

The rocket will reach 1,200 feet on its way up in 2 seconds and on the way down in 38 seconds.

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An arrow is shot vertically upward at a rate of 220 feet per second. Use the projectile formula h = −16 t 2 + v 0 t to determine when height of the arrow will be 400 feet.

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Everyday math

A bullet is fired straight up from a BB gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula h = −16 t 2 + v 0 t + 8 to determine how many seconds it will take for the bullet to hit the ground. (That is, when will h = 0 ?)

70 seconds

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A city planner wants to build a bridge across a lake in a park. To find the length of the bridge, he makes a right triangle with one leg and the hypotenuse on land and the bridge as the other leg. The length of the hypotenuse is 340 feet and the leg is 160 feet. Find the length of the bridge.

The image shows a right triangle with a horizontal side stretching across a lake, a vertical side on the left labeled a and the hypotenuse connecting the two.
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Writing exercises

Make up a problem involving the product of two consecutive odd integers. Start by choosing two consecutive odd integers. What are your integers? What is the product of your integers? Solve the equation n ( n + 2 ) = p , where p is the product you found in part (b). Did you get the numbers you started with?

answers will vary
answers will vary answers will vary answers will vary

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Make up a problem involving the product of two consecutive even integers. Start by choosing two consecutive even integers. What are your integers? What is the product of your integers? Solve the equation n ( n + 2 ) = p , where p is the product you found in part (b). Did you get the numbers you started with?

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has two rows and four columns. The first row is a header row and it labels each column. The first column is labeled

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Practice Key Terms 2

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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