Factoring
Factor x2 + 4x + 3
(x + 3)(x + 1)
Solve (x-3)(x+5)=0
x = 3, -5
The monthly profit of a gym is shown by p(d)=-7d2+77d-100, where d is the price of a membership. Write an equation that shows the gym making $500 in profit per month.
500=-7d2+77d-100
What would a quadratic with zero real solutions look like on a graph? Sketch an example!
No x-intercepts.
Write the equivalent standard form quadratic to (2x-1)(x+4)
2x2 + 4x - 4
Factor x2 -7x + 10
(x-5)(x-2)
Solve x2+3x+2 = 0
x = -1, -2
Which equation represents finding the time that it takes an object to hit the ground?
a. -16t2 + 430t + 20 = 1000
b. -16t2 + 430t + 20 = 0
c. -16t2 + 430t + 20 = -50
b. -16t2 + 430t + 20 = 0
Why do you set quadratic equations equal to zero to solve them?
Because solving means finding the x-intercepts of the function and y = 0 at the x-intercepts.
a. x2 + 6x = 19
b. x2 + 6x + 9 = 10
c. x2 + 6x + 9 = 19
Factor 36x2 - 81
(6x+7)(6x-7)
Solve 2x2 + 4x - 3 = 0
x = [-4 +/- sqrt(40)]/4
A rocket's height is modeled by the equation
h(t) = -16t2 + 200t + 40
How long does it take for the rocket to hit the ground?
12.7 seconds
Why wouldn't you solve 4x2=20x by dividing by x?
Because you eliminate x = 0 as a solution (since you can't divide by zero!)
What must you add to make x2 + 8x + 11 a perfect square?
5
Factor 16x2+100
Not factorable
Solve (x - 4)2 = 11
x = 4 +/- sqrt(11)
The profit of a musical is modeled by the equation
p(d) = -8d2 +80d - 20
What is the maximum profit that the theater can make?
$180
Why would you rewrite a standard form quadratic as a perfect square?
Like (x - 3)2 = 16
So that you could easily solve by taking the square root of both sides!
Explain why x2+12x+10=0 is equivalent to x2+12x+36=26
Because you added 26 to both sides, which is legal in math!
Factor (4/81)x2 - 121
((2/9)x + 11)((2/9)x - 11)
Solve -5x2+11x-4
x = [-5 +/- sqrt(41)]/-10
A rocket's height is modeled by the equation
h(t) = -16t2 + 200t + 40
How long does it take to reach its maximum height and what is its maximum height?
6.25 seconds. 665 feet
When asked to solve 4x2 + 44x = 0, Jordan factored into 4x(x + 11) = 0. Why would she do this?
So that she can use the zero product property to set each factor equal to zero and solve for x.
Write the perfect square equation that is equivalent to x2 + 0.5x = 8
x2 + 0.5x + 0.25 = 8.25