Factoring
Solve the following quadratic equation from factored form.
(2x-1)(x+5)=0
x = 1/2 x = -5
Solve the following quadratic equation by using square roots:
x2 = 4
x = 2 x = -2
Solve using any method
x2-x-10 = 2
x=4 and x = -3
Simplify -√-32
-4i√2
√x7
x3√x
Solve the following quadratic equation by factoring.
2x2 - 12x + 10 = 0
x = 5 x = 1
Solve the following quadratic equation by using square roots:
x2 = -121
+11i or -11i
Solve the following quadratic equation:
4x2 + 5x = 11
x = (-5 ± √201)/8
If the discriminant is a negative number, what type of solutions does the quadratic equation have?
2 complex solutions
Simplify √-148
2i√37
Solve the following quadratic equation by factoring.
x2 - 6x - 24 = 3
x = 9 x = -3
Simplify √112
4√7
Solve the following quadratic equation by using any method:
5x2 = -x + 4
x = 4/5 and x = -1
Based on the factored form of y=(x+3)(x+3) and the vertex form y=(x+3)2, what can you conclude about the graph of the parabola?
The vertex and x-intercept are both at (-3,0)
Solve the system of equations
y=x2+4
y=2x+3
(1,5)
When solving by factoring, why must the equation be set equal to zero first?
The y-value of the x-intercepts is zero and the solutions are represented by the x-intercepts.
Solve the following quadratic equation by using square roots:
(x - 6)2 - 9 = 0
x = 9 and x = 3
Solve the following quadratic equation by using any method: 2x2 - 8x - 17 = 0
x = (4 ± 5√2)/2
Solve the system of equations
y=x2-4x+6
y=x+2
(1,3) and (4,6)
A car manufacturer does performance tests on its cars. The equation that models the distance the first car travels is: d =1.16t2 and the equation for the second car is d = 1.74(t - 3)2, where t is time in seconds, after the first car starts the test and d is the distance in meters. At what time will both cars have driven the same distance?
16.34 seconds and 1.66 seconds
Solve the following quadratic equation by factoring.
2x2 - 5x - 3 = 0
x = -1/2 x = 3
Solve the following quadratic equation by using square roots:
(x+7)2 + 9 = 5
x = -7 ± 2i
Solve the following quadratic equation by using the quadratic formula:
8x2 + 4 = 4x
x = (1 ± i√7)/4
if i = √-1, what is i4?
i2 = -1 so i4=1
The height, h of a baseball, in meters at t seconds after it is tossed out of a window is modeled by: h = -5t2 +20t +15. A boy shoots at the baseball with a paintball gun. The trajectory of the paintball is given by the equation: h = 3t + 3. Will the paintball hit the baseball? If so, when?
Yes. 4 seconds.