1. Chapter 2 – Polynomial and Rational Functions
2.1 – Quadratic Functions

2. This function is the polynomial function
The a’s are constants (normal numbers)
The x’s are variables
This polynomial is of degree n
What do we call a polynomial of degree 1?
Linear!
What do we call a polynomial of degree 2?
Quadratic!

3. Properties of a quadratic function:
If a is positive, the parabola opens upward
If a is negative, the parabola opens downward
(0, c) is the y-intercept
Ex: How does the graph of the function below relate to the graph of y = x2 ?
y = -5(x+3)2 + 1
This function is shifted left 3 units,
shifted up 1 unit,
stretched by a factor of 5,
and flipped vertically
(opens downward)

4. Vertex form for a quadratic function:
(h, k) is the vertex
x = h is the line of symmetry
To convert to standard form, complete the square!
Ex: Write y = x2 – 4x + 5 in vertex form.
Look at the first 2 terms and complete the square
To do that, divide the b by 2 and square it!
Since we added 4, we have to subtract 4 at the end…
Then complete the square!

5. Ex: Write y = 2x2 + 4x – 8 in vertex form.
Separate the first 2 term, then factor out a 2 from the first two terms…
Divide the second term by 2 and square it…
Since we added 2 1’s, we have to subtract 2 at the end…
Then complete the square!

6. Ex: Write y + 5 = -3x2 + 15x in vertex form.

7. Write the equation in vertex form:
Notice that the vertex is always at !

8. Write an equation in vertex form of a parabola with vertex (2,-3) passing through (5, 66).

9. If factoring doesn’t work, use quadratic formula!
Ex: Find the x-intercepts of y = x2 – 4x – 5 .
To find the x-intercepts, find where y = 0
Factor!!!
When factored, we see that our x-intercepts are at x = -1 and x = 5.
If factoring doesn’t work, use quadratic formula!