Show:
Factoring to Calculate the Roots
Key Features of Quadratics by using Desmos
Quadratics in
the Real World
100

Factor to calculate the roots to the following quadratic:

x2 - 5x - 14 = 0

x = 7 x = -2

100

What is the y-intercept for the quadratic function?

x2 + 5x - 12 = y

y-intercept = -12

100

1. 

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function y=-16x2+16x+480, where x is the time in seconds and y is the height in feet.


How long did it take for Jason to reach his maximum height?

.5 seconds

200

Factor to calculate the roots to the following quadratic:

 x2 + 3x + 2 = 0

x = -2 x = -1

200

What are the roots the quadratic function?

x2 - 6x + 12 = 0

no roots

200


Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function y=-16x2+16x+480, where x is the time in seconds and y is the height in feet.


What was Jason's maximum height?

484 ft

300

Factor to calculate the roots to the following quadratic:

x2 - 6x + 5 = 0

x = 5 x = 1

300

What is the vertex for the quadratic function?

x2 - 5x - 14 = 0

(2.5, -20.25)

300

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function y=-16x2+16x+480, where x is the time in seconds and y is the height in feet.


What is the height of the cliff?

480 ft

400

Factor to calculate the roots to the following quadratic:

x2 - 6x - 27 = 0

x = 9 x = -3

400

What is the line of symmetry for the parabola?

2x2 + 4x - 8 = 0

x = -1

400

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function y=-16x2+16x+480, where x is the time in seconds and y is the height in feet.


How long did it take for Jason to reach the water?

6 seconds

500

Factor to calculate the roots to the following quadratic:

 2x2 - 5x - 3 = 0

x = -1/2 x = 3

500

Calculate the y-intercept, vertex, roots, and line of symmetry for the quadratic.

x2 + 2x - 6 = 0

y-intercept: -6

vertex: (-1, -7)

roots: -3.646 and 1.646

line of symmetry: x = -1

500

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function y=-16x2+16x+480, where x is the time in seconds and y is the height in feet.

Why does only one root make sense with this word problem?

You cannot have negative time.