Quadratic word problems Algebra-2 Quadratic word problems

Quiz Factor: 1. 2.

Real World What path does the cannon ball take? Any object in freefall and subject to gravitational field travels in a parabolic path.

Projectile Motion A vertical time-distance problem in two dimensions. Height as a function of time. Height at time = 0 (initial height) Vertical component of acceleration (of Gravity) multiplied by time squared gives the change in vertical position due to gravity. Vertical component of velocity (speed) multiplied by time gives the change in vertical position resulting from the initial velocity.

The projectile motion equation for units in feet and seconds. Don’t worry, I’ll give you the equation with the numbers in it. In Pre-Calculus and math 1050 you’ll have to come up with the equation on your own. Height at time = 0 (initial height) Vertical component of acceleration Vertical component of velocity

Projectile Motion Problem An object is launched vertically upward from the ground at an initial velocity of 250 ft per second. When will the object reach its maximum height? b. What is the object’s maximum height? c. When will the object fall back down to the ground?

Projectile Motion Problem An object is launched vertically upward from the ground at an initial velocity of 250 ft per second. When will the object reach its maximum height?

Projectile Motion Problem An object is launched vertically upward from the ground at an initial velocity of 250 ft per second. When will the object reach its maximum height? (7.8, 976.6): Which is time? Which is height? b. What is its maximum height?

Projectile Motion Problem An object is launched vertically upward from the ground at an initial velocity of 250 ft per second. c. When will the object fall back to the ground? (15.6, 0) Which is time? Which is height?

Your turn: 1. When will the object reach its maximum height? An object is launched vertically upward from the top of a 100 foot building at an initial velocity of 175 ft per second. 1. When will the object reach its maximum height? 2. What is the object’s maximum height? 3. When will the object fall back down to the ground?

Projectile Motion Problem An object is launched vertically upward from the ground at an initial velocity of 250 ft per second. When will the object reach its maximum height? b. What is its maximum height? (5.5, 578.5): Which is time? Which is height?

Projectile Motion Problem An object is launched vertically upward from the ground at an initial velocity of 250 ft per second. c. When will the object fall back to the ground? (11.5, 0) Which is time? Which is height?

Your turn: An object is launched vertically upward from the ground at an initial upward velocity of 123 ft per second. 4. When will the object reach its maximum height? 5. What is the object’s maximum height? 6. When will the object fall back down to the ground?

Your turn: 7. An object is launched vertically dropped of the edge of a cliff. The cliff is 1500 feet high. When will the object fall to the ground? 8. An airplane drops a bomb from an altitude of 20,000 feet. How long does it take for the bomb to fall to the earth?

Your turn: 9. An annoying kid throws a water balloon off of his balcony at a girl below. The balloon’s initial vertical velocity is 10 feet per second downward. The balcony is 50 feet above the sidewalk. When will the water balloon reach the sidewalk beside the girl ? (he was a bad shot)

Solve a totally non-recognizable quadratic equation. By the zero product property, x = -3, 2 Can’t use the zero product property Your turn: 10. Find the right side x-intercept for the following quadratic equation:

Solve a totally non-recognizable quadratic equation. By the zero product property, x = -3, 2 Can’t use the zero product property Your turn: 11. Find the right side x-intercept for the following quadratic equation:

Your turn: 12. Write an expression for the following: “three more than twice a number” 13. Write an expression for the following: “two less than a number”

Finding the dimensions of a rectangle. The length of one side of a rectangle is three more than two times a number. What is the expression for the length of the side? The width of the rectangle is two less than the number. What is the expression for the length of the side? x - 2 2x + 3 If the area of the rectangle is 400 square inches, what is the length and width of the rectangle?

Finding the dimensions of a rectangle. A = 400, length = ? Width = ? By substitution: x - 2 By substitution: 2x + 3 By substitution:

Solve a totally non-recognizable quadratic equation. Can’t use the zero product property Your turn: 14. Find the x-intercepts for the following quadratic equation: 15. Use the values of x that you found in #10 to find the length of the rectangle. 16. Use the values of x that you found in #10 to find the width of the rectangle.

Vocabulary x > 3 and x < 5 1 2 3 4 5 Compound inequality Hint: This can also be written as: 3 < x < 5 Hint: Inequality with “and” looks like:   1 2 3 4 5

Projectile motion: A pebble is thrown upward with an intial velocity of 25 feet per second from ground level. For what period of time will it be above 5 feet? “and” type inequality

Projectile motion: A pebble is thrown upward with an intial velocity of 25 feet per second from ground level. For what period of time will it be above 5 feet?

Projectile motion: A pebble is thrown upward with an intial velocity of 25 feet per second from ground level. For what period of time will it be above 5 feet? 0.24 sec 1.33 sec

When above a certain height? An arrow is shot upward with an intial velocity of 250 feet per second from ground level. For what period of time will the arrow be above 1000 feet? Never gets above 1000 feet

When above a certain height? An arrow is shot upward with an intial velocity of 250 feet per second from ground level. For what period of time will the arrow be above 500 feet?

Your turn: 17. When will it hit the ground? A ball is dropped from the roof of a 500 foot building. 17. When will it hit the ground? 18. For what period of time is the ball above 400 feet? 19. When will the object be below 100 feet above ground level?

Summary: Projectile Motion 1. Find the maximum height (y-value of the vertex) Time to reach the maximum height (x-value of the vertex) 3. Find the time to fall back to the ground (x-intercept)

Summary: 4. Finding the dimensions of the bottom of a box. Non-standard quadratic equation. Put into standard form and solve for ‘x’, then use ‘x’ to find the length and the width of the box.

Summary: Projectile Motion 5. Find the time period when the box is above 200 feet. Use two equations. One of the equations is “y = 200” Solve graphically. Use intersections to find when the object is exactly at 200 Write the inequality for the value of time (x-values) when the object is above 200 feet.