Graphing Quadratic Functions
Find the Vertex and Axis of Symmetry of the equation
g(x)=−3x^2+6x−9
AOS x = -1
Vertex = (-1,-6)
(a) what is the height of the ball after 1 second
(b) what is the maximun height of the ball
(a) 40 meters
(b) 1.75 sec or 7/4
Evaluate
i^54
Solve the inequality 4x^2 + x- 3> 0.
(−∞,−1]∪[43,∞)
Solve for x
2x^2 = 48
x = plus or minus 2 root 6
Create a Table of following equation
x^2 - 2x - 3
A Rocket is fired from the top of a 100ft tower at a velocity of 40 ft/sec. the height h(t) of the rocket, t seconds after firing is given by h(t) = -16t^2 + 40t + 100.
Whats the max height reached by the rocket?
125 ft
simplify
root -156
2i root 39
Find c to create a perfect square trinomial, then change into a perfect square
x^2 - 22x + C
C = 121
(x - 11)^2
Convert g(x)=−3^2+6x−9 into vertex form.
g(x)=−3(x−1)2−6
The Simsbury Garden, measuring 12 m by 16 m, is to have a uniform pedestrian pathway installed all around it, increasing the total area to 285 square meters. Find the width of the walkway.
Width = 1.5 meters
Simplify
(5 - 14i) + (-18 - 21i)
-13 - 35i
Graph on coordinate plane
Y < -x^2 + 5
y < x^2 + 3x -4
https://www.desmos.com/calculator
(Plug into Desmos)
Solve by completing the square
x^2 + 4x -12 = 0
x = 2
x = -6
Describe all the transformations from the parent function to change f(x)=x^2 to g(x)=−3(x−1)^2−6.
Reflection across the x-axis, vertical stretch by a factor of 3, horizontal shift 1 unit right, and vertical shift 6 units down.
You are building a rectangular garden for the Simsbury Farmers Market. You have exactly 40ft of fencing to enclose three sides of the garden, using a pre-existing brick wall at the Simsbury Meadows Performing Arts Center as the fourth side. What are the dimensions that will create the maximum possible area for the garden.
Dimensions are 10 x 20, maximum area 200ft^2
Find the roots of the equation
x^2 - 6x + 10
x = 3 + i
x = 3 - i
A rectangular parking lot must have a perimeter of 240ft and an area of at least 3600 square feet. find the possible lengths of the parking lot.
Lengths of Parking lot are 60 and 60
Give at least 2 example values for K when the equation x^2 + 5x + K has 2 real solutions and must be a positive whole number
1,2,3,4,5,6
Change into vertex form while also listing transformation steps, vertex, and axis of symmetry.
g(x) = 12x^2 - 48x + 53
12(x-2)^2 + 5
Vertex = (2,5)
AOS x= 2
A Vertical stretch by 12, a horizontal shift of 2 to the right and a vertical shift of 5 upwards
During a science class field trip, Maya launches a model rocket straight up into the air from a launching pad. The height of the rocket, h (in meters), at any given time, t (in seconds), after launch is modeled by the quadratic equation: -5t^2 + 40t -5 = h
(a) Find the amount of time for the rocket to reach 35 meters on its way down
(b) how long it will take the rocket to reach the ground
(b) (8 + 2 root 17)/2,
Evaluate
(7 - 11i)/(3 + 4i)
-(23 + 61i)/25
A model rocket is launched vertically upward from a platform 10 feet off the ground. Its height h (in feet) over time t (in seconds) is modeled by the function h(t) = -16t^2 + 80t + 10
How long is the rocket above 74ft?
between 1 and 4 seconds
1 ≤ t ≤ 4
Solve by Completing the Square
3x^2 + 7x -4
x = (-7 - root 97)/6 and x = (-7 + root 97)/6