Quadratic Formula
What is the Quadratic Formula?
x=(-(b)+-sqrt((b)^2-4ac))/(2a)
Salvador hits a baseball at a height of 3 ft and with an initial velocity of 88 feet per second. The equation y=-16x^2+88x+3 represents the baseball's height as a function of time where x represents time in seconds after the ball is hit, and y represents the height of the ball in feet.
What does the 3 represent in this context?
The initial height of the ball was 3 feet before he hit it.
Which method would you use to solve the following quadratic? State it, then solve.
4x^2-36=0
Inverse operations or factoring.
x=3 and x=-3
Convert the following quadratic to vertex form using any method.
y=x^2-2x-5
y=(x-1)^2-6
What continent has the most people?
Asia
Solve the following quadratic using the Quadratic Formula:
2x^2-5x+3=0
x=1 and x=3/2 or 1.5
Salvador hits a baseball at a height of 3 ft and with an initial velocity of 88 feet per second. The equation y=-16x^2+88x+3 represents the baseball's height as a function of time where x represents time in seconds after the ball is hit, and y represents the height of the ball in feet.
What is the vertex, and what does it mean in context to the problem?
(You can use Desmos).
Vertex: (2.75, 124)
After 2.75 seconds, the ball reaches a maximum height of 124 feet.
Which method would you use for solving the following quadratic? State the method and solve.
x^2+2x-15=0
Factoring.
x=-5 and x=3
Convert the following quadratic to standard form.
y=-2(3x-1)(x+7)
y=-6x^2-40x+14
Which country has won the most men's World Cups?
Brazil
Solve the following quadratic using the Quadratic Formula:
3x^2-6x=-3
x=1
Salvador hits a baseball at a height of 3 ft and with an initial velocity of 88 feet per second. The equation y=-16x^2+88x+3 represents the baseball's height as a function of time where x represents time in seconds after the ball is hit, and y represents the height of the ball in feet.
What are the roots of this equation? What do they mean in context of the problem?
x~~-0.03382 and x~~5.5339
The baseball hits the ground after 5.5339 seconds. **The negative solution doesn't make sense due to not being able to have negative time.**
Which method would you use to solve the following quadratic? State the method and then solve.
x^2+16x+10=0
Quadratic Formula.
x=-8+-3sqrt6
Convert the following quadratic to factored form.
y=2x^2-15x+28
y=(2x-7)(x-4)
Who did the UVM Men's Soccer team get defeated by in the playoffs this year?
Hofstra
Solve the following quadratic using the Quadratic Formula:
8x^2-18=4x
x=(1+-sqrt(37))/4 or x~~-1.2707 and x~~1.7707
Salvador hits a baseball at a height of 3 ft and with an initial velocity of 88 feet per second. The equation y=-16x^2+88x+3 represents the baseball's height as a function of time where x represents time in seconds after the ball is hit, and y represents the height of the ball in feet.
When will the ball be 24 feet above the ground?
After 0.25 seconds and 5.25 seconds.
Which method would you use to solve the following quadratic? State the method and then solve.
5x^2+30x=0
Factoring or Quadratic Formula.
x=-5 and x=3
Convert the following quadratic to vertex form.
y=-2(x-6)(x+9)
y=-2(x+1.5)^2+112.5
What is the coldest temperature ever recorded in Vermont?
-50 degrees
Solve the following quadratic using the Quadratic Formula:
8x^2+6x=-5
No Real Solution
If 200=-16x^2+88x+3 , what is your solution?
There are no real solutions.
The ball will never reach 200 feet.
Which method would you use to solve the following quadratic? State the method and then solve.
-4(x-5)^2+484=0
Inverse Operations.
x=-6 and x=16
Convert the following quadratic to factored form.
y=5(x+0.5)^2-11.25
y=5(x+2)(x-1)
As of July 1, 2024, about how many people live in Colchester, VT?
17,807