1. Wilawan Srithong Nakhonsawan School
Parabola
Wilawan Srithong
Nakhonsawan School

2. Contents 1 Introduction Quadratic Equation Standard Form of Parabola 23

3. What is Parabola?

4. What is Parabola?
Ball
Parabolas are the shapes that define projectile motion (the path that a ball takes when it is hit or thrown into the air).

5. Quadratic Equation General form: f(x) = ax2 + bx + c where a ≠ 0
ax2  Quadratic Term
bx  Linear Term
c  Constant Term
Vertex (highest point)
Vertex (lowest point)
a>0: Parabola opens upward
a<0: Parabola opens downward

6. Standard Equation f(x) = ax2 Simple form of Parabola Standard Equation
The vertex of this equation is (0,0)
a>0: Parabolas open upward
a<0: Parabolas open upward

7. Standard Equation
Parabola Standard Equation
y = ax2 
y = a(x-h)2 + k

8. Example 1 Graph the quadratic function
We begin by identifying values for a, h, and k
Standard form
a=-2 h=3 k=8
Given function

9. Example 1 Step1 Step2 Step3 Determine how the parabola opens.
a, the coefficient of x2 is-2.
Thus, a<0
The parabola opens downwards.
Find the x-intercepts by solving
Step1
Step2
Step3
Find the vertex.
The vertex of the parabola is at (h,k)
the parabola has its vertex at (3,8)

10. Example 1
Step 3
Find the x-intercepts by solving
The x-intercepts are 1 and 5. The parabola passes through (1,0) and (5,0)

11. Example 1 Step4 Step5 Find the y-intercept by computing f(0)
The parabola passes through (0,-10)
Step5
Graph the parabola

12. Example 2 Step1 Step2 Graph the quadratic function f(x)=-x2-2x+1.
Use the graph identify the function’s domain and its range.
Step1
Determine how the parabola opens.
The coefficient of x2, is -1 (a<0)
 Parabola opens downward
Step2
Find the vertex.
The x-coordinate of the vertex is
We identify a, b, and c in

13. Example 2
Substitute -1 for a and -2 for b into the equation for the x-coordinate :
The x-coordinate of the vertex is -1 and the vertex is at (-1,f(-1))
We substitute -1 for x in the equation of the function,
to find the y-coordinate:

14. Example 2 Step3 The parabola passes through (-2.4,0) and (0.4,0)
Find the x-intercepts by solving
The parabola passes through (-2.4,0) and (0.4,0)

15. Example 2 Step4 Find the y-intercept by computing f(0)
The parabola passes through (0,1)

16. Example 2
Step5
Graph the parabola

17. Thank you for your kind attention