Vertex Form
y = a(bx - h)^2 + k
What is the order of operations to write transformations in (when given an equation)?
- Horizontal Shifts
- Stretches/Compressions
- Reflections
- Vertical Shifts
How many points make a parabola?
Three
If a transformation occurs outside the parenthesis, what does it apply to?
Ex: 2f(x)
Everything outside the parenthesis
If a transformation occurs inside the parenthesis, what does it apply to?
Ex: f(2x)
It only replaces the x-value
What are the steps to graphing an equation in vertex form?
f(x) = a(bx - h)^2 + k
- Find the vertex (h, k)
- Find the axis of symmetry (x = h)
- Plug a value into the original equation. Plot the point.
- Create another point equidistant from the axis of symmetry.
What are the steps to graphing in standard form?
ax^2 + bx + c
- Find the line of symmetry. (-b/2a).
- Find the vertex by plugging in the x-value from line of symmetry back into the equation.
- Find more points.
How do you find the axis of symmetry when given standard form?
ax^2 + bx + c
-b / 2a
How do you find the y-intercept when given standard form?
ax^2 + bx + c
(0, c)
What is the minimum/maximum value of a parabola?
The y value of the vertex
What are the steps to graphing in intercept form?
f(x) = a (x-p)(x-q)
- Find the x-intercepts. (p, 0) and (q, 0)
- Find the axis of symmetry: p+q/2.
- Plug in the x-value to find the vertex.
- Plot all the points.
Outside the parenthesis. Greater than one.
Vertical stretch
Outside the parenthesis.
Less than one.
Vertical shrink
Inside the parenthesis. Greater than one.
Horizontal shrink of the RECIPEROCAL value.
Inside the parenthesis. Less than one.
Horizontal stretch of the RECIPEROCAL value
Describe the transformation: f(2x)
Horizontal Shrink of 1/2.
Describe the transformation: f(1/2x)
Horizontal Stretch of 2
Intercept Form
y = a (x-p)(x-q)
Standard Form
ax^2 + bx + c
