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Vertex, Intercept, Domain, Range of Quadratic Function

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1. Given the quadratic equation y=-x^2+2x+8, find:
a) the vertex
b) the axis of symmetry
c) the intercepts
d) the domain
e) the range
f) the interval where the function is increasing and
g) the interval where the function is decreasing
h) graph the function
y=-x^2+2x+8

2. The following polynomial represents a profit function for a certain production line, where x is a number of produced units, find
a) the zeros and multiplicity of each
b) where the graph crosses or touches the x-axis
c) number of turning points
d) explain the meaning of the above if any,
f(x)=(x-4)^2(x^2-25)

Solution Preview

1. a=-1 b=2 c=8
a. vertex: x=-b/2a=1
b. x=-1
c. x-intercept: (-2,0) and (4,0), y-intercept: (0,8)
d. domain: all real numbers
e. range: (negative infinity, 8]
f. the interval where the ...

Solution Summary

The solution gives detailed steps on finding vertex, axis of symmetry, intercept, domain, range, increasing/decreasing interval for a given quadratic function. The graph with function is also included for deep understanding. Also, an application regarding the above concepts is answered in details.

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