Question

Consider the parabola to the right to determine each of the following:

a. Explain whether the function has a maximum value or minimum value.
b. Determine the minimum or maximum value and where it occurs.
c. Identify the vertex.
d. Identify the axis of symmetry.
e. Identify the function’s domain and range.
f. Find the equation of the parabola.
The graph may not be exact.
I will attached the graph once I get to the response area because it will not let me copy and paste.Please somebody help me quick.

Answer 1

a) Ok, so it turns at a minimum point (low peak)
b) by looking at the graph, I would say (-3,-6)
c) This is a parabola - the vertex is the turning point (-3,-6)
d) This is the x value of the vertex so axis: x = -3
e) domain: all real x (its just a parabola)
range: all real y ≥ -6
f) So it cuts at (lets say) 1.25 and -7.25. So the equation has factors (x-1.25)(x+7.25)
now test x = -3, do we get -6?
(-3-1.25)(-3+7.25) = -4.25*4.25 = 18.0625 which is (289/96) of what we expected.
So multiply (x-1.25)(x+7.25) by 96/289 to get equation.

Equation: 96(x-1.25)(x+7.25)/289

Please note these are values read off a graph (perhaps inaccurately) so don't just get the answers but see what I did.

Answer 2

Graph:

Answer 3

Okay did you use the graph I provided? Or can you show me the graph you use co I can see how you came up with those answers?

Answer 4

okay thanks.

Answer 5

Yeah I looked at your graph, then graphed my equation to check