1. Factor each polynomial. 𝑥 2 −16 3 𝑥 2 +7𝑥+2 3 𝑥 4 +9𝑥
Bell work
Factor each polynomial.
𝑥 2 −16
3 𝑥 2 +7𝑥+2
3 𝑥 4 +9𝑥
Solve each quadratic equation.
𝑥 2 −8𝑥+12=0

2. Quadratic Equations
𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐

3. The shape produced by a quadratic function is called a parabola.

4. Solving a quadratic equation
What are the solutions to a quadratic equation?
Roots
X-intercepts
Zeros (or zeros of the function)
Methods used to solve quadratic equations:
Factoring
Square root method
Quadratic formula
Graphing
Completing the square

5. Graphing a Quadratic Graph 𝒚= 𝒙 𝟐
Use a table of coordinates to graph the parabola. X
𝒚= 𝒙 𝟐 Y -2
𝑦= −2 2 -1
𝑦= −1 2
𝑦= 0 2 1
𝑦= 1 2 2
𝑦= 2 2

6. Graphing a Quadratic Graph 𝒚= −𝟐𝒙 𝟐 +𝟑 X 𝒚= −𝟐𝒙 𝟐 +𝟑 -2 𝑦= −2 −2 2 +3Y -2
𝑦= −2 − -1
𝑦= −2 −
𝑦= − 1
𝑦= − 2
𝑦= −

7. Key features of a Parabola
The vertex is either the maximum or minimum point on the graph. It is the point were the graph changes direction.
The axis of symmetry is a line (not part of the graph) that goes through the vertex so that the graph of the parabola is mirrored on the other side.
The roots (or x-intercepts) are the points where the parabola intercepts the x-axis

8. General form of a quadratic function
𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐 𝑦=2 𝑥 2 −4𝑥+1
State a, b, and c for the following:
𝑦= 𝑥 2 −2𝑥+4
𝑓 𝑥 = 𝑥 2 +8𝑥+10
𝑦= 𝑥 2 −4𝑥+5

13. Which type of roots?
Two real roots
One real root (repeated)
No real roots

14. Which type of roots?
Two real roots
One real root (repeated)
No real roots

15. Which type of roots?
Two real roots
One real root (repeated)
No real roots

16. Which type of roots?
Two real roots
One real root (repeated)
No real roots