Vertex, Intercept, Domain, Range of Quadratic Function

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.

See the attached problems
1. find the intercept,vertex,domain, and range, then graph the parabola
(1) y = x^2 + 2x - 3
(2) y = -x^2 -5x - 4
(3) a = b^2 -6b - 16
2. graph the parabola, state the domain and range:
(1) y = 1/3x^2 - 6
(2) y= -x^2 -1
(3) y = (x - 2)^2

Find all real or imaginary solutions to each equation: 3v^2 + 4v - 1 = 0
Solve the equation
2y^2 - 3y - 6 = 0
(x-10)(x-2) = -20
Determine whether the parabola opens up or down: y = -1/2x^2 + 3
Find the vertex and intercepts for each parabola: g(x) = x^2 + x - 6
Find all real solutions to each equation: x^2 + x +

9 practice problems on quadratic equations in the attached file.
8)a)Solve 7x+x(x-2)=0
b)Find the x-intercepts of f(x)=7x+x(x-2)
15) Find the vertex, the line of symmetry, the maximum or minimum value of the quadraticfunction and graph the function: f(x)=2x2-8x+6
(21) Solve by completing the square
(23) Find the vertex,

Please see the attached file - Don't mind the graphing portion, work what can be worked. I have to input answers not write out the whole equation.
7. Find the vertex, line of symmetry, and the maximum or minimum value of a quadraticfunction, and graph the function.f(x) = -x +6x +2
The vertex is
8. Find the vertex,lin

F(x) = 2x^2 - 8x, where x = or > 2
Even though I know that this particular quadratic equation does have an inverse since the domain is limited, I don't know how to figure out the formula for the inverse for a quadratic equation. I don't know how to solve for x, since there are two different x's.
Thank you!