Vertex to Standard Form
Convert to standard form.
y=(x-5)2-4
y=x2-10x+21
x2=196
x=-14,14
Pretend Parentheses are absolute value bars.
(x)+5=12
x=7,-7
A diver jumps off of a 30ft tall diving board at with an initial velocity of 1 ft per second. How long until he hits the water?
1.4 Seconds
A kitchen needs to be 200 square feet. The length is 10 ft longer than the width. Set up the equation you would graph on your calculator.
x(x+10)-200
Convert to standard form.
y=2(x-5)2-15
y=2x2-20x+35
(x-8)2=400
x=-12,28
Pretend Parentheses are absolute value bars.
(6x-12)=60
x=-8,12
A superhero jumps from a 10 foot platform over a building at 25 ft per second. If the building is 20 ft tall, will he make it? Why or why not?
No, his maximum height is only 19.8 ft.
A gymnasium needs to be 115 square feet. The length is 8 ft longer than the triple width. Set up the equation you would graph on your calculator.
x(3x+8)-115
Convert to Standard Form
y=1/2(x-4)2-3
1/2x2-4x+5
-5(x-6)2-20=-100
x=10,2
Pretend Parentheses are absolute value bars.
(10x-7)-15=-2
x=-0.6,2
What is the projectile motion formula?
H(t)=-16t2+v0t+h0
A driveway's length is 4 meter more than twice the width. The total area is 160 meters. Find x and the extraneous solution.
x=8, (-10,0) is extraneous
What is the vertex form equation?
What is the standard form equation?
y=a(x-h)2+k
y=ax2+bx+c
4(-x-5)2+30=46
x=-7,-3
Pretend Parentheses are absolute value bars.
5(3x-2)-15=110
x=9,-7.7
A ball is thrown from ground level at 40 ft per second. Find and interpret both the maximum and x intercept.
The ball will reach a max height of 25 ft after 1.25 seconds. The ball will hit the ground at 2.5 seconds.
A patio is 40 square meters. The length is 3 meters more than the width, find the dimensions.
5 m wide by 8 m ft long.
List the 3 steps to putting an equation in Standard Form.
Ex: y=3(x-4)2-10
-Expand the binomial
-Distribute the Coefficient
-Combine like terms
1/2(2x-4)2-10=40
x=7,-3
Pretend Parentheses are absolute value bars.
3/4(-4x-8)-30=0
x=-12,8
Lily jumps 20 ft per second from a 5 foot platform. Oliver jumps 30 ft per second from the ground. How much longer will it take Oliver to hit the ground after Lily?
0.4 Seconds
A pool has an area of 83.25 yards. The length is 5 yards more than 3 times the width. Find the dimensions of the pool.
4.5 Yards by 18.5 Yards