Quadratic Basics
What does a function need to have in order to be quadratic?
What is x2
What is the standard form of a quadratic function?
Give examples.
f(x)=ax2+bx+c
f(x)=x2
g(x)=x2+4
h(x)=5x2+3x+8
Which is factored form of a quadratic function?
Give examples.
f(x)=a(x-p)(x-q)
f(x)=(x-4)(x+2)
g(x)=x(x+1)
Does the function f(x)=x2+2x+1 have a minimum or maximum?
minimum
What is the shape of the graph of a quadratic function called?
Parabola
What does the constant value tell you about a quadratic function in standard form?
f(t)=-16t^2+40t+8
y-intercept or starting amount
What information does factored form give you?
The x-intercepts
How is the function f(x)=-x2 transformed?
opens downward
What is the highest or lowest point of a parabola called?
Vertex
Capital of Mexico
Mexico City
Which continent is home to the Sahara desert?
Africa
Which country is known as the Land of the Rising Sun?
Japan
Name 2 things that will change about your graph when you multiply the x^2 term by -10.
-10x^2
x^2
Will flip upside down and become more steep/skinnier
How wide (diameter) is a basketball hoop?
18 inches (1.5 feet)
Find the vertex
f(x)=(x-4)(x+2)
(1,-9)
How is the function g(x)=0.5x2+1 transformed compared to f(x)=x2?
The function is wider and moved up by 1
What are the x-intercepts of this function?
Double points for finding the x-coordinate of the vertex also.
g(x)=(x-1)(x-5)
(1,0) and (5,0)
X-coordinate of the vertex is 3 (halfway between x-intercepts).
Find the y-intercept
f(x)=-3(x-5)(x+3)
(0,45)