Results 1 to 3 of 3

Thread: help intercepts

  1. #1
    Newbie
    Joined
    Jan 2019
    From
    toronto
    Posts
    18

    help intercepts

    2. Which of the following parabolas opens upward and appears narrower than y=−3x ^2 +2x−1 ?
    o A. y= 4x^2 −2x−1
    o B. y= − 4x^2 +2x−1
    o C. y= x^2 +4x
    o D. y= − 2x^ 2 +x+3

    Answer:
    A

    CORRECT OR NOT

    3. Which of the following parabolas is 2 units higher than y=2x^ 2 −4x−1 , but has the same shape and opens in the same direction?
    o A. y=2x^ 2 −6x−1
    o B. y=2x^ 2 −2x−1
    o C. y=2x^ 2 −4x−3
    o D. y=2x^2 −4x+1

    Answer
    D

    CORRECT OR NOT


    4. What are the coordinates of the vertex of the parabola y=x ^2 +2x−1 ?
    o A. (−2,5)
    o B. (−1,−2)
    o C. (−2,−1)
    o D. (−1,2)

    Answer
    B

    CORRECT OR NOT


    5. Which of the following equations has an axis of symmetry with the equation x=1.5 ?
    o A. y=2x^ 2 −6x−1
    o B. y=2x^ 2 −3x+1
    o C. y=x ^2 +6x−3
    o D. y=2x^ 2 +3x+2

    Answer
    A

    CORRECT OR NOT

    THANKS MUCH
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,568
    Thanks
    2900

    Re: help intercepts

    2. correct
    3. correct
    4. correct
    5. correct

    well done
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    20,249
    Thanks
    3366

    Re: help intercepts

    Quote Originally Posted by yorkmanz View Post
    2. Which of the following parabolas opens upward and appears narrower than y=−3x ^2 +2x−1 ?
    o A. y= 4x^2 −2x−1
    o B. y= − 4x^2 +2x−1
    o C. y= x^2 +4x
    o D. y= − 2x^ 2 +x+3

    Answer:
    A

    CORRECT OR NOT
    Correct. A parabola opens upward if and only if its leading coefficient (the coefficient of $x^2$) is positive so it cannot be B or D. A parabola is "narrower" if the absolute value of its leading coefficient is larger. |4|> |-1| while |1| is not

    3. Which of the following parabolas is 2 units higher than y=2x^ 2 −4x−1 , but has the same shape and opens in the same direction?
    o A. y=2x^ 2 −6x−1
    o B. y=2x^ 2 −2x−1
    o C. y=2x^ 2 −4x−3
    o D. y=2x^2 −4x+1

    Answer
    D

    CORRECT OR NOT
    Correct.
    A parabola is "2 units higher" if its y value is 2 more. Adding 2 to $\displaystyle 2x^2- 4x- 1$ gives $\displaystyle 2x^2- 4x+ 1$.

    4. What are the coordinates of the vertex of the parabola y=x ^2 +2x−1 ?
    o A. (−2,5)
    o B. (−1,−2) ………
    o C. (−2,−1)
    o D. (−1,2)

    Answer
    B

    CORRECT OR NOT
    Correct. Complete the square by adding and subtracting 1:
    $\displaystyle y= x^2+ 2x+ 1- 1- 1= (x+ 1)^2- 2$. When x= -1, y= -2. For any other x, $\displaystyle (x+ 1)^2$ is positive so $\displaystyle y= (x+ 1)^2- 2$ is larger than -2. The vertex is (-1, -2).


    5. Which of the following equations has an axis of symmetry with the equation x=1.5 ?
    o A. y=2x^ 2 −6x−1
    o B. y=2x^ 2 −3x+1
    o C. y=x ^2 +6x−3
    o D. y=2x^ 2 +3x+2

    Answer
    A

    CORRECT OR NOT
    Complete the square in each.
    $\displaystyle 2x^2- 6x- 1= 2(x^2- 3x+ (9/4)- (9/4))- 1= 2(x- 3/2)^2- 9/2- 1= 2(x- 3/2)^2- 11/2$. The vertex is (3/2, -11/2) so the axis of symmetry is x= 3/2.
    $\displaystyle 2x^2- 3x+ 1= 2(x^2- (3/2)x+ 9/16- 9/16)+ 1= 2(x- 3/4)^2- 9/8+ 1= 2(x- 3/4)^2- 1/8$. The vertex is (3/4, -1/8) so the axis of symmetry is x= 3/4.
    $\displaystyle x^2+ 6x- 3= x^3+ 6x+ 9- 9- 3= (x+ 3)^2- 12$. The vertex is (-3, -12) so the axis of symmetry is x= -3.
    $\displaystyle 2x^2+ 3x+ 2= 2(x^2+ 3x+ 9/4- 9/4)+ 2= 2(x+ 3/2)- 9/2+ 2= 2(x+ 3/2)^2- 5/2$. The vertex is (-3/2, -5/2) so the axis of symmetry is x= -3/2.

    THANKS MUCH
    It would be better if, in the future, instead of just posting your answers, you also post the work you did to get that answer as I did above.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Feb 23rd 2011, 03:46 AM
  2. Y intercepts
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Apr 13th 2010, 09:58 AM
  3. intercepts
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Feb 14th 2009, 05:37 AM
  4. Intercepts. Please Help.
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Sep 25th 2008, 06:29 PM
  5. x and y intercepts
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 19th 2008, 10:31 AM

/mathhelpforum @mathhelpforum