LHS CAT4e ISM-10-final

LHS CAT4e ISM-10-final - Chapter 10 ANALYTIC GEOMETRY...

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1027 Chapter 10 ANALYTIC GEOMETRY Section 10.1: Parabolas 1. (a) The relation () 2 24 yx −= + has vertex ( ) 4, 2 and opens up, so the correct choice is D. (b) The relation 2 42 has vertex ( ) 2, 4 and opens up, so the correct choice is B. (c) The relation 2 −= − + has vertex ( ) 4, 2 and opens down, so the correct choice is C. (d) The relation 2 has vertex ( ) 2, 4 and opens down, so the correct choice is A. (e) The relation 2 xy has vertex ( ) 2, 4 and opens to the right, so the correct choice is F. (f) The relation 2 has vertex ( ) 4, 2 and opens to the right, so the correct choice is H. (g) The relation 2 has vertex ( ) 2, 4 and opens to the left, so the correct choice is E. (h) The relation 2 has vertex ( ) 4, 2 and opens to the left, so the correct choice is G. 2. (a) Since the variable x is squared, we know that the parabola will either open up or down. Since y is isolated and the coefficient of the 2 - x term is positive, we know the parabola must open up. Thus, the correct answer is B. (b) Since the variable x is squared, we know that the parabola will either open up or down. Since y is isolated and the coefficient of the 2 - x term is negative, we know the parabola must open down. Thus, the correct answer is D. (c) Since the variable y is squared, we know that the parabola will either open to the left or to the right. Since x is isolated and the coefficient of the 2 - y term is positive, we know the parabola must open to the right. Thus, the correct answer is A. (d) Since the variable y is squared, we know that the parabola will either open to the left or to the right. Since x is isolated and the coefficient of the 2 - y term is negative, we know the parabola must open to the left. Thus, the correct answer is C. 3. 22 100 0 10 x y x y −= ⇒ =− ⇒ =− + ⇒ − =− The vertex is ( ) 0,0 . The graph opens to the left and has the same shape as 2 = . The domain is ( ] ,0 . −∞ The range is ( ) ,. −∞ ∞ The graph is symmetric about its axis, the horizontal line 0 y = (the x- axis). Use the vertex and axis and plot a few additional points. x y 4 2 1 1 0 1 1 4 2 4. 02 2 0 x y x y −= ⇒= +⇒ =− +⇒−=− The vertex is ( ) 2,0 . The graph opens to the right and has the same shape as 2 = . It is a translation 2 units to the right of the graph of 2 = . The domain is [ ) 2, . The range is ( ) −∞ ∞ The graph is symmetric about its axis, the horizontal line 0 y = (the x- axis). Use the vertex and axis and plot a few additional points. ( continued on next page )
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1028 Chapter 10: Analytic Geometry ( continued from page 1027 ) x y 6 2 3 1 2 0 3 1 6 2 5. () 22 30 3 xy x y =− ⇒−=− The vertex is ( ) 0,3 . The graph opens to the right and has the same shape as 2 = . It is a translation 3 units up of the graph of 2 = . The domain is [ ) 0, . The range is ( ) ,. −∞ ∞ The graph is symmetric about its axis, the horizontal line 3. y = Use the vertex and axis and plot a few additional points.
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This note was uploaded on 11/13/2010 for the course MATH MAT 123 taught by Professor Smith during the Spring '10 term at Thomas Edison State.

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LHS CAT4e ISM-10-final - Chapter 10 ANALYTIC GEOMETRY...

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