Quadratic Basics
What does a function need to have in order to be quadratic?
What is x2
What does vertex form of a quadratic function look like?
f(x)=a(x-h)2+k
What is the standard form of a quadratic?
f(x)=ax2+bx+c
Which is factored form of a quadratic function?
f(x)=a(x-r1)(x-r2)
Does the function f(x)=x2+2x+1 have a minimum or maximum?
minimum
What is the graph of a quadratic function called?
Parabola
What is the vertex
f(x)=2(x-4)2+3
(4,3)
What formula do you use to find the axis of symmetry in standard form?
-b/2a
What should you find and graph first when given a function in standard form?
The x-intercepts
How is the function f(x)=-x2 transformed?
opens downward
What is the absolute maximum or absolute minimum point on a parabola?
Vertex
Find the axis of symmetry
f(x)=-2(x+3)2+1
x=-3
What does the c-value tell you is standard form?
y-intercept
Find the axis of symmetry
f(x)=2(x-3)(x-7)
x=5
How is the function f(x)=x2+3 transformed?
moves up 3
Name 2 things that the a-value in standard form tell you about the shape of the parabola?
Opens up or down, narrow or wide
Find the y-value when x=2
y=2x2-3x+3
y=5
Find the axis of symmetry
f(x)=2x2+8x-3
x=-2
Find the vertex
f(x)=(x-4)(x+2)
(1,-9)
How is the function f(x)=.5x+1 transformed?
The function is wider and moved up by 1
Which of these functions have an axis of symmetry at x=2 (could be more than 1)
a. f(x)=-2x2+8x-3
b. g(x)=(x-1)(x-5)
c. h(x)=2(x-2)2+1
a. and c.
Find the y-intercept of teh function
f(x)=-2(x-1)2-1
(0,-3)
Find the vertex
f(x)=x2-4x+1
(2,-3)
Find the y-intercept
f(x)=-3(x-5)(x+3)
(0,45)
How is the function f(x)=-2x2-7 transformed?
the parabola open down, is more narrow, and moved down 7