Factoring (ch. 8.1)
factor x2 +5x-14
(x+7)(x-2)
find the vertex of y=(x+3)2-5
(-3,-5)
use the quadratic formula to solve x2+3x+1
x=-0.382
x=-2.618
What is minimum and maximum?
Minimum is the lowest piece of data in the set. Maximum is the highest piece of data in the set.
factor 4x2-9
(2x+3)(2x-3)
What is the most important information needed for graphing and which forms of a quadratic are the best to find each?(standard, vertex/graphing, factored)
x int.:factored form
y int.:standard form
vertex:vertex/graphing form
solve for x with zero product property:
(2x+3)(3x-7)=0
x=-1.5
x=2 1/3
Find the center, spread, max, min, q1, and q3 of this data
8, 7, 6, 7, 3, 9, 6, 9, 9
center:median-7
spread: IQR-3
Q1:6 Q3:9
Min:3 Max:9
factor 16x2+8x+1
(4x+1)(4x+1)
Find the x intercepts, y intercept, and vertex of this equation:
y=x2-2x-24
x int.:(-4,0)(6,0)
y int.:(0.-24)
vertex:(1,-25)
solve for x with completing the square:
y=(x+2)2-9
x=1
x=-5
When would you use mean and standard deviation?
When the set of data is symmetrical.
factor x2+4x+60
not factorable
put this equation into vertex/graphing form:
y=x2-8x+19
y=(x-4)2+3
find x with the zero product property
x2+11x-60=0
x=-15
x=4
what do spread and center show?
center:shows the average or "typical" data of the set
Spread: shows how consistent the set of data is
factor 30x2+135x-270
15(x+6)(2x-3)
A parabola shows the path of a rocket (x-axis as time, Y-axis as height). What would the x intercepts mean in this context?
The x intercepts would show when the rocket touches the ground.
when would you use the quadratic formula, zero product property, and completing the square
Quadratic formula: when the equation is unfactorable
Completing the square: when in vertex/graphing form
Zero product property: when factorable
Why do we use median and IQR with skewed data?
It gives a more accurate representation of spread and center because it is resistant to outliers.