Quadratic Equations

Projectile Motion

100

What is the initial velocity and the starting height in the equation h(t)=-16t²+24t+5?

v₀=24

h₀=5

200

At what time does a ball reach maximum height if the flight of the ball is modeled by  h(t)=-16t²+24t+30 ?

t = 0.75 seconds

300

What is the maximum height a ball will reach if the flight of the ball is modeled by  h(t)=-16t²+24t+30 ?

What is 39 feet?

400

When does the rocket hit the ground if the rocket is launched from 3 feet off the ground with an initial velocity of 315 ft/sec and modeled by h(t)=-16t²+315t+3

At 19.70 seconds

500

Write a projectile motion equation for a soccer ball that is punted 2 feet off the ground with an initial velocity of 12 ft/sec.

What is h(t)=-16t²+12t +2?

Square Roots

100

Solve the following quadratic equation by using square roots: x² = 4

x = 2 x = -2

200

Solve the following quadratic equation by using square roots: x² = 121

+11 or -11

300

Solve the following quadratic equation by using square roots: 4x² = 400

x = 10 x = -10

400

Solve the following quadratic equation by using square roots: x² -9 = -8

1 or -1

500

Solve the following quadratic equation by using square roots: 5(x - 4)² + 3 = 128

x = 9 x = -1

Discriminant or i

100

Simplify:

sqrt(-4)

2i

200

Find the discriminant and number and type of solutions

x^2+2x-3=0

16, two real solutions

300

Find the discriminant and number and type of solutions.

x² - 2x - 24 = 0

100, two real solutions

400

Simplify 

sqrt(-147)

7i sqrt(3)

500

Find the discriminant and number and type of solutions

-3x^2=11x+14

-47, Two imaginary solutions

Quadratic Formula

100

What is the quadratic formula?

x = (-b +- sqrt(b^2 - 4ac)) /(2a)

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1 x = -5

300

Solve the following quadratic equation by using the quadratic formula: x² - 9x + 20 = 0

x = 5 x = 4

400

Solve the following quadratic equation by using the quadratic formula:

 2x² + 11x + 4 = 0

x=(-11+- sqrt(89))/4

500

Solve the following quadratic equation by using the quadratic formula: -4x² = 17x + 15 

x = -3 x = -5/4

Find The Vertex

100

Find the vertex of

f(x)=-x²+8x-15

(4,1)

200

Find the vertex of

f(x)=-3(x-2)^2-4

(2,-4)

300

Find the vertex of 

f(x)=5x²+4

(0,4)

400

Find the vertex of

h(t)=-16x² +48x+10

(1.5,46)

500

Find the vertex of 

h(t)=-4.9t²+12.8t+6

(1.31,14.36)