The function in vertex form f ( x ) = a ( x − h ) 2 + k of the function f ( x ) = − 2 x 2 + 4 x + 6

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Answer 1

Question

Chapter 3, Problem 3RE

(a)

To determine

To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

(b)

To determine

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

(c)

To determine

To Calculate: The vertex of f(x)=−2(x−1)2+8.

(d)

To determine

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

(e)

To determine

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

(f)

To determine

To Graph: The sketch of the function f(x)=−2x2+4x+6.

(g)

To determine

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

(h)

To determine

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

(i)

To determine

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

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ے ملزمة احمد Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to- one iff (f(x1),f(x2),...,f(x) } linearly independent. (b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a hyperplane of X. مبر خد احمد Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is convex set or not, affine set or not. Write with prove an application of Hahn-Banach theorem. Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)

Let M be a proper subspace of a finite dimension vector space X over a field F show that whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M or not. (b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L prove convex subset of X and hyperspace of X. Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA. (b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there Xiff there exists fE X/10) and tE F such that M=(xE X/ f(x)=t). (c) Show that the relation equivalent is an equivalence relation on set of norms on a space X.

Q/(a)Let X be a finite dimension vector space over a field F and S₁,S2CX such that S₁SS2. Show that whether (1) if S, is a base for X then base for X or not (2) if S2 is a base for X then S, is a base for X or not (b) Show that every subspace of vector space is convex and affine set but the conevrse need not to be true. allet M be a non-empty subset of a vector space X over a field F and x,EX. Show that M is a hyperspace iff xo+ M is a hyperplane and xo€ xo+M. bState Hahn-Banach theorem and write with prove an application about it. Show that every singleten subset and finite subset of a normed space is closed. Oxfallet f he a function from a normad roace YI Show tha ir continuour aty.GYiff

Answer 2

Question

Chapter 3, Problem 3RE

(a)

To determine

To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

(b)

To determine

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

(c)

To determine

To Calculate: The vertex of f(x)=−2(x−1)2+8.

(d)

To determine

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

(e)

To determine

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

(f)

To determine

To Graph: The sketch of the function f(x)=−2x2+4x+6.

(g)

To determine

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

(h)

To determine

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

(i)

To determine

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

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Answer 3

Question

Chapter 3, Problem 3RE

(a)

To determine

To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

(b)

To determine

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

(c)

To determine

To Calculate: The vertex of f(x)=−2(x−1)2+8.

(d)

To determine

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

(e)

To determine

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

(f)

To determine

To Graph: The sketch of the function f(x)=−2x2+4x+6.

(g)

To determine

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

(h)

To determine

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

(i)

To determine

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 3, Problem 3RE

(a)

To determine

To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

(b)

To determine

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

(c)

To determine

To Calculate: The vertex of f(x)=−2(x−1)2+8.

(d)

To determine

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

(e)

To determine

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

(f)

To determine

To Graph: The sketch of the function f(x)=−2x2+4x+6.

(g)

To determine

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

(h)

To determine

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

(i)

To determine

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 3, Problem 3RE

(a)

To determine

To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

(b)

To determine

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

(c)

To determine

To Calculate: The vertex of f(x)=−2(x−1)2+8.

(d)

To determine

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

(e)

To determine

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

(f)

To determine

To Graph: The sketch of the function f(x)=−2x2+4x+6.

(g)

To determine

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

(h)

To determine

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

(i)

To determine

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

Answer 6

Chapter 3, Problem 3RE

(a)

To determine

To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

Answer 7

Chapter 3, Problem 3RE

(a)

To determine

To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

Answer 8

(b)

To determine

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

Answer 9

(b)

To determine

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

Answer 10

(c)

To determine

To Calculate: The vertex of f(x)=−2(x−1)2+8.

Answer 11

(c)

To determine

To Calculate: The vertex of f(x)=−2(x−1)2+8.

Answer 12

(d)

To determine

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

Answer 13

(d)

To determine

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

Answer 14

(e)

To determine

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

Answer 15

(e)

To determine

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

Answer 16

(f)

To determine

To Graph: The sketch of the function f(x)=−2x2+4x+6.

Answer 17

(f)

To determine

To Graph: The sketch of the function f(x)=−2x2+4x+6.

Answer 18

(g)

To determine

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

Answer 19

(g)

To determine

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

Answer 20

(h)

To determine

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

Answer 21

(h)

To determine

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

Answer 22

(i)

To determine

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

Answer 23

(i)

To determine

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

Answer 24

Expert Solution & Answer

Answer 25

Expert Solution & Answer

Answer 26

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Answer 27

Ch. 3.1 - Prob. 1SP Ch. 3.1 - Prob. 2SP Ch. 3.1 - Prob. 3SP Ch. 3.1 - Prob. 4SP Ch. 3.1 - Prob. 5SP Ch. 3.1 - Prob. 6SP Ch. 3.1 - Prob. 1PE Ch. 3.1 - Prob. 2PE Ch. 3.1 - Prob. 3PE Ch. 3.1 - Prob. 4PE

The function in vertex form f ( x ) = a ( x − h ) 2 + k of the function f ( x ) = − 2 x 2 + 4 x + 6

Concept explainers

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To Calculate: The function in vertex form f(x)=a(x−h)2+k of the function f(x)=−2x2+4x+6

To Calculate: Whether the graph of the parabola f(x)=−2x2+4x+6 opens upward or downward.

To Calculate: The vertex of f(x)=−2(x−1)2+8.

To Calculate: The x-intercept(s) of f(x)=−2x2+4x+6.

To Calculate: The y-intercept of f(x)=−2x2+4x+6.

To Graph: The sketch of the function f(x)=−2x2+4x+6.

To Calculate: The axis of symmetry of the vertex (h,k) is (1,8) for f(x)=−2x2+4x+6

To Calculate: The minimum or maximum value of the function f(x)=−2(x−1)2+8.

To Calculate: The domain and range of the function f(x)=−2x2+4x+6.

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Chapter 3 Solutions