1 Factor each polynomial. 𝑥 2 −16 3 𝑥 2 +7𝑥+2 3 𝑥 4 +9𝑥Bell 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 equationWhat 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 𝟐Use 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 ParabolaThe 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 function𝑓 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

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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