Graph analysis of a parabola
Maximum and minimum
We have that the maximum is the largest value the function takes vertically (for y)
The minimum is the smallest value the function takes.
In this case:
It reaches its maximum when x = 0 at y = 18
It reaches its minimum when x = 4 at y = 0.
Then
Max: x = 0
Min: x = 4
Vertex and axis of symmetry (AOS)
We have that the axis of symmetry is the line that cuts the parabola into equal halves. The vertex is the point where the line is cut:
In this line the axis of symmetry (AOS) is located on x = 2
The vertex is the point (x, y) = (2, 18)
Vertex = (2, 8)
AOS: x = 2
Intercepts
y- intercept:
The y axis is always intercepted when x = 0.
Here, the point where x = 0 shows the height in the second 0. It is to say, the height where the rock in launched.
Then, the y - intercept represents that the rock was launched from a height of 10.
x- intercept:
The y axis is always intercepted when y = 0.
Here, the point where y = 0 shows the second when the height is 0. It is to say, the second when the rock lands on the ground.
Then, the x - intercept represents that the rock was lands on the ground 4.5 seconds adter being launched.
Domain and range
We have that the domain is the set of x- values the function takes:
In this case it goes from
x = 0 to x = 4.5
The range is the set of y- values the function takes:
In this case it goes from
y = 0 to y = 18
domain = [0, 4.5]
range = [0, 18]
Additional questions
We have that after 4 seconds is when x = 4
When x = 4 then y = 10.
We have that when the rock reaches its max height x = 2.
When y is the max then x = 2.
