Question

The illustration below shows the graph of yyy as a function of xxx.

Answer 1

• quadratic or parabola function
  (both are same; do not know what the answer choices are)
  
• 
  `y =\boxed{ 0}`
  
• 
  `\textrm{x = \boxed{0} \;and x = \boxed{6}}`
  
• 
  `\textrm{The greatest value of y is y = \boxed{9} and occurs when x = \boxed{3}}`
  
• 
  `\textrm{For x between x = \boxed{0} and x = \boxed{6}, the function value $y \;\boxed{\ge} \;0$}`
  (my best guess not knowing the answer choices

Explanation:

Answer 2

• It is a quadratic function.
• The y-intercept is y = 0.
• The x-intercepts are x = 0 and x = 6.
• the greatest value of y is 9 when x = 3.
• between x = 0 and x = 6, we have y ≥ 0.

How to complete the statements?

First, this clearly is the graph of a parabola (also called a quadratic equation).

Then, the y-intercept is the value at which the graph intercepts the vertical axis, the value at which this happens is at y = 0.

Finally, we have two x-intercepts, these are the values of x at which the graph intercepts the horizontal axis, we can see that these happen at:

x = 0

x = 6

Then, the greatest value of y is at the vertex, we can see that the vertex is at (3, 9)

Finally, in the interval (0, 6) the graph is above the horizontal axis, so it is positive.