Question

The illustration below shows the graph of y as a function of x.

Answer 1

Answer:

• parabola

• y = -6
• x=2 and x=6
• Greatest value of y is y=2 and it occurs when x = 4
• For x between x = 2 and x = 6, y > 0

Step-by-step explanation:

Definition

• A parabola is a curve where any point is at an equal distance from:

               a fixed point (the focus ), and

               a fixed straight line (the directrix )

From the graph we can see that this is indeed so. We can even calculate the parabola equation from the given graph but since that is not required, I am not illustrating the steps here to do that

• The y-intercept is the value of y where the parabola cuts the y axis and from the graph we see that this occurs at y = -6

• The x-intercepts are the x-values where the parabola crosses the x-axis and we can see that this occurs at x = 2 and x = 6

• The greatest value of y occurs at the vertex of the parabola and we see that the vertex is at (4,2) ie greatest value of y is at y = 2 and occurs at x=4

• Between x =2 and x = 6 we see that the y values greater than 0 ie y > 0

(Note on last question: If you exclude these two points then y > 0 between x=2 and x=6.Specifically it is 0 at x =2 and x=6 and > 0. So if you include these two points then y ≥ 0.  I have taken it as excluding the two points, x = 2 and x =6)