Graphing Functions
What axis will the x intercepts always be on?
X-Axis
How many x-intercepts can a quadratic have?
0, 1 or 2
What is the standard form of a quadratic?
y=ax2+bx+c
**Can easily see the y-intercept
Write an equation in factored form when x=-4, 12
y=(x+4)(x-12)
If my graph only touches the x-axis once, what is that point also called?
The Vertex
How do you write the axis of symmetry?
x= x coordinate of vertex
What is the factored form of a quadratic?
y=a(x+b)(x+c)
**Can easily see the x-intercepts
Write an equation in standard form with the following x-intercepts. (2,0) (6,0)
y=x2-8x+12
How do you find the vertex if you know both x intercepts?
Add them together and divide by two.
To find the y intercept what do you plug in for x?
Zero
What is vertex form of a quadratic?
y=a(x+h)2+k
**Can easily see the vertex
Write an equation in vertex form when x=2,9
y=(x-5.5)2 +12.25
How do you draw the axis of symmetry on a graph?
A dashed line.
How do you write the X-intercepts/Y-intercept
How do you change from standard form to vertex form?
Completing the square
Rewrite y=x2+8x-9 in vertex form.
y=(x+4)2+25
If you have a graph with x-intercepts what do you need to do to the x-coordinate to write it in factored form?
Flip the sign. ex: positive becomes negative
What are three methods we know to finding the x-intercepts?
Zero Product property (diamond boxing)
Completing the square to solve for X
Quadratic Formula
Rewrite 4(x-1)2-2 in STANDARD FORM
4x2-8x+2