Discriminant
What is the formula for the discriminant?
b2 - 4ac
What method is the best for solving this quadratic
x2+6x+9=0
Factoring (Add Multiply)
Solve
x2-5x-14=0
{7,-2}
The equation h=-16t2+198t+25 represents the height of a diver (in feet) jumping off a cliff after t seconds. What is the height of the cliff?
25 feet
Initial Height --> y-intercept
Solve for x:
|x-6| = 12
x = 18 and x = -6
What does the discriminant tell us?
How many roots a quadratic has
What method is the best for solving this quadratic
-2(x-8)2 - 32 = 12
Solving Symbolically (Roots in Vertex Form)
Solve
x2-4x+4
{2}
The equation h=-16t2+198t+25 represents the height of a diver (in feet) jumping off a cliff after t seconds. When does the diver reach their maximum height?
Round to the nearest tenth (you can use a calculator if needed)
6.2 sec
h value of the vertex (-b/2a)
Solve for x:
|x-5| + 9 = 26
x = 22 and x = -12
Use the discriminant to find how many roots the following quadratic has: 3x2 - 4x - 12
Two roots (discriminant: 160)
What method is the best for solving this quadratic
2x2-18=0
Factoring (Take GCF, then Add Multiply)
Solve
2x2+2x-12
{2,-3}
The equation -15t2+60t+3 represents the height of a water balloon at t seconds. How long will it take for the water balloon to hit the ground?
You can use a calculator if needed
4.05 seconds
Find the roots (quadratic formula). Larger root is the time it takes to hit the ground
Solve for x:
4|x+3| - 11 = 25
x = -12 and x = 6
Use the discriminant to determine how many roots the equation has: 2x2 - 8x +11
No Real Roots (discriminant -72)
What method is the best for solving this quadratic
2x2+3x-5
Quadratic Formula
Solve (round to the nearest tenth)
4x2+8x+3
{-.5,-1.5}
The equation P=-3x2+12x+2 represents the amount of P profit for the x cost of an item. What is the maximum profit for the sale if the item?
$14
'k' value of the vertex
h = (-b/2a). Plug in 'h' for x into the original equation to find the 'k' value
Solve
-|2x - 9| = -13
x = 11 and x = -2
Use the discriminant to determine how many roots the equation has: 5x2 - 10x +5
One Root (Discriminant 0)
What method is the best for solving this quadratic
3x2 - 4=0
Quadratic Formula
Solve (round to the nearest hundredth)
9x2+4x-16
{1.13, -1.57}
-16t2+64t+120 represents the height of a rocket at t time in seconds. How long does it take the rocket to reach 40ft?
You can use a calculator if needed)
1 second
-16t2-64t+120= 40
Subtract 40 from both sides and solve using quad formula
Solve for x:
5|x+14| - 2 = 50
x = -3.6 and x = -24.4