Complete the Square
For x2-10x-5=0, what is the value of c when you are completing the square?
c=25
What are the roots of 0=x(x+1)?
x=____ and x=_____
x=0 and x=-1
For f(x)=a(x-h)2+k, what does k represent and what is it's formula?
Maximum height, k=f(h)
f(x)=(x)2+4 is created from f(x)=x2 by which transformations? You MUST state them in mathematical language.
Language bank: horizontal/vertical shift, horizontal stretch/shrink, reflection over x-axis, reflection over y-axis.
Vertical shift 4 up.
The equation f(x)=a(x-h)2+k is in ______ form.
Vertex
For x2+2x=-3, what is the value of c when you are completing the square?
1
What are the roots of the equation 0=(x+3)(x-4)?
x=____ and x=_____.
x=-3 and x=4
Which measures maximum height?
Possible answers:
h
k
roots
k
f(x)=(x-3)2 is created from f(x)=x2 by which transformations? You MUST state them in mathematical language.
Language bank: horizontal/vertical shift, horizontal stretch/shrink, reflection over x-axis, reflection over y-axis.
Horizontal shift 3 to the right.
If I want to know when a ball hit the ground, I am looking for the positive ______.
Possible answers: root, zero, x-intercept, solution.
For x2+8x+2=0, what do you need to add to each side of the equation to complete the square?
16, because c=16
To find the "root(s)" of an equation means to solve for ____.
x
Where is the vertex on any given graph? Write your answer as a coordinate point, i.e. the vertex is ( , ).
(h,k)
f(x)=-(x)2 is created from f(x)=x2 by which transformations? You MUST state them in mathematical language.
Language bank: horizontal/vertical shift, horizontal stretch/shrink, reflection over x-axis, reflection over y-axis.
Reflection over the x axis.
What is the formula for h?
-b/2a
For x2-4x=8, what do you need to add to each side of the equation to complete the square?
4, because c=4
What are the roots of the equation 0=(x+2)(3x-9)?
x=-2, x=3
What is the maximum height of a soccer ball (in meters) portrayed by the function f(x)=(x+1)2+12?
12 meters
f(x)=-(x)2-2 is created from f(x)=x2 by which transformations? You MUST state them in mathematical language.
Language bank: horizontal/vertical shift, horizontal stretch/shrink, reflection over x-axis, reflection over y-axis.
Reflection over x-axis, vertical shift down 2.
What are 3 ways to find solutions to quadratic equations? Using the _____, ______ or _______.
Quadratic Formula
Completing the Square
Factoring
For x2=6x-7, what do you need to add to each side of the equation to complete the square?
9, because c=9
The roots of the function 0=2x2-x-1 are x=___ and x=___.
x=1 and x=-1/2
What is the maximum height of a soccer ball portrayed by following table, where t is time in seconds and f(t) is distance in feet?
t l -1 l 0 l 1 l 2 l
f(t) l 3 l 5 l 7 l 5 l
7 feet
f(x)=-(x+1)2+4 is created from f(x)=x2 by which transformations? You MUST state them in mathematical language.
Language bank: horizontal/vertical shift, horizontal stretch/shrink, reflection over x-axis, reflection over y-axis.
Reflection over x-axis, horizontal shift 1 to the left, vertical shift 4 up.
What are three other words that mean the same thing as the "roots" of an equation?
Solutions
Zeros
x-Intercepts