Parabolas
By DarthVader
Date: 2022-07-03
Topic: 142 see comments
Post views: 1122
Parabolas
Interactive graph: https://learn2.open.ac.uk/mod/oucontent/view.php?id=1906321&extra=thumbnail_idm60
The graph of any quadratic function of the form y = ax2 + bx + c has the shape of a parabola.
To find y-intercept:
Set x equal to zero to get y = c, which is the y-intercept.
To find x-intercept(s):
Use the quadratic formula to find all the solutions for the x-intercept(s).
To find vertex (line of symmetry) x-point:
x = −(b / 2a)
To find vertex y-point:
Set x equal to the vertex x-intercept and solve for y.
The number of solutions of a quadratic equation:
The value b2 − 4ac is called the discriminant of the quadratic expression ax2 + bx + c .
The quadratic equation ax2 + bx + c = 0has:
- two solutions if b2 − 4ac > 0 (the discriminant is positive)
- one solution if b2 − 4ac = 0 (the discriminant is zero)
- no real solutions if b2 − 4ac < 0 (the discriminant is negative).
U-Shaped Or N-Shaped
- Parabola is ‘u-shaped’ if the coefficient of ‘a’ is positive, and n-shaped if it is negative.
- All parabolas are symmetrical around an axis of symmetry that splits the parabola in half with a vertical line that cuts through the x-axis. This is called the vertex.
Finding the maximum height of a vertically launched projectile:
h = −0.5gt2 + v0t + h0
where:
h0 = initial height (m)
v0 = initial velocity (m s-1)
t = time (s)
g = gravity (m s-2)
To find the maximum height, calculate the y coordinate of the vertex.
Time taken from start to finish is found by calculating the x intercepts of the equation.
| Comments | Creator | Date | ID |
|---|
