Quadratic Functions and Parabolas

1. Quadratic Functions and Parabolas Present by Michael Ai

2. Quadratic Equations Standard form: ax²+bx+c=0 a≠0, where a,b,c are real numbers discriminant: b²-4ac≥0, if b²-4ac<0, the equation doesn't exist. We can solve the quadratic equations by completing squares, factoring and using the quadratic formula

3. Standard Forms of Quadratic Functions Function: y=ax²+bx+c, a≠0 where a,b,c are real numbers. Vertex form: y=a(x-h)²+k, Vertex(h,k) Zeros: The zeros of quadratic functions is are the solutions of associated quadratic equation.

4. Analyze the Graphs 1. The graph of a quadratic function is a parabola (Vertical Axis) 2. The graph opens up if a>0, and down if a<0. 3. Vertex: (h,k) or (-b/2a,f(-b/2a)) 4. x=h, or x=-b/2a as the axis of symmetry 5. The function has minimum value, if a>0. The function has maximum value, if a<0.

5. Graphs

6. Quadratic images from our life

7. Parabola A parabola is a mirror symmetrical curve in a plane equidistant from a fixed line(the directrix) and a fixed point not on the line (the focus).

8. Vertical Major Axis Parabola Standard Equation (with vertex(0,0) and directrix y=-p ): x²=4py, focus: (0,p), Standard Equation (with vertex (h,k) ): (x-h)²=4p(y-k), focus: (h, k+p), directrix: y=k-p

9. Graphs

10. How does it relate to Quadratic Functions? standard equation of a parabola quadratic equation: y=(x-h)²/4p +k

11. Images of parabolas from our life

12. Summary The purpose of this project is helping us to review the quadratic chapter and parabolas. Those formulas are not very complex, but they are important basic formulas which can help us to understand the advanced level math.

13. Thank you!