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Social Science8. For the quadratic functions a. f(x) = -3z2 6x - 1, b. g(x) =2x1(a) Find the vertex form. What is the vertex? (b) Find the x and y intercepts of the above function.(c) Find the domain and the range(d) Find the maximum or the minimum.(e) Write a brief verbal description of the relationship between the graphof the above quadratic and the graph of h(x) x2.
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8. For the quadratic functions a. f(x) = -3z2 6x - 1, b. g(x) = 2x1 (a) Find the vertex form. What is the vertex?
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(b) Find the x and y intercepts of the above function. (c) Find the domain and the range (d) Find the maximum or the minimum. (e) Write a brief verbal description of the relationship between the graph of the above quadratic and the graph of h(x) x2.
Expert Answer
As per our policy I am solving 1st three subparts and for the remaining subparts post the question again separately.
Given,
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-3x26x - 1 and g (x) = -x2 2x1 f(x)
Part a
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3x2 + 6x - 1 f (x) -3(x2 — 2х) — 1 3(x2 2x 1 - 1) 1 (adding and subtracting 1) - -3((x -1)2 -1) -1 — — 3 (х — 1)2 + 3 — 1 — — 3 (х — 1)2 + 2 So, the vertex form of f(x) is -3(x -1)2 2 and vertex of f(x) is (1,2)
And
...
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g(x)-x2 - 2x + 1 - -(x2 2x) 1 -(x2 2x 1- 1)+ 1 (adding and subtracting 1) ((1)2 1) + 1 -(x + 1)2 + 1 +1 = -(x + 1)2 + 2 -(x + 1)2 2 and vertex of f (x) is (-1,2) So, the vertex form of g (x) is
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