1. Given f(x)=-2(x-1)^{2}+8 a. Determine whether the graph o

druczekq4

druczekq4

Answered question

2021-12-07

1. Given f(x)=2(x1)2+8
a. Determine whether the graph of the parabola opens upward or downward
b.Identify the vertex
c.Determine the x-intercept(s)
d.Determine the y-intercept
e.Sketch the function
f.Determine the axis of symmetry
g.Determine the maximum or minimum value of f
h.Write the domain and range in interval notation.
2. From the graph of the quadratic function f(x)=(x+2)29, determine the equation of the symmetry
3. Determine the x-intercept(s) of the quadratic function f(x)=x2+10x+26

Answer & Explanation

Himin1945

Himin1945

Beginner2021-12-08Added 12 answers

Calculation:
1)
Part a)
The general equation of parabola is,
f(x)=a(xh)2+k
where (h, k) shows the vertex.
Equation given in the problem is shown below,
f(x)=2(x1)2+8
Here a=2, it means parabola will be opening downward.
Part b)
After comparing,
The vertex of the given parabola is (1, 8).
Part c)
The intercept at x-axis will be calculated by placing y equals to zero.
2(x1)2+8=y
2(x1)2+8=0
2(x1)2=8
2(x1)2=8
(x1)2=4
x1=±2
x=1,3
So the x-intercepts are (-1, 0) and (3, 0).
Part d)
The intercept at y-axis will be calculated by placing x equals to zero,
2(x1)2+8=y
2(01)2+8=y
2(1)2+8=y
2+8=y
y=6
So, the y-intercept is (0, 6).
Part e)
The graph of the function is shown below,
Part f)
The axis of symmetry is given by,
x=b2a
Now,
Taking the given parabola equation,
f(x)=2(x1)2+8
=2(x22x+1)+8
=2x2+4x24+8
=2x2+4x+6
From above equation,
a=2,b=4,c=6
x=42(2)
x=1
So, the axis of symmetry is x=1.
Part g)

Taking the given function,
f(x)=2(x1)2+8
f(x)=4(x1)
fx)=4
So,
f"(x) clearly suggests that it has maximum and no minimum,
So,
f(x)=4(x1)
4(x1)=0
x1=0
x=1
The maximum is found when f(x)=0.
So,
f(x)=4(x1)
4(x1)=0
x1=0
x=1
The maximum value of given function is,

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