1. ## 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

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

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)

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

A

CORRECT OR NOT

THANKS MUCH

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

well done

3. ## Re: help intercepts

Originally Posted by yorkmanz
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

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

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)

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

$\displaystyle 2x^2- 6x- 1= 2(x^2- 3x+ (9/4)- (9/4))- 1= 2(x- 3/2)^2- 9/2- 1= 2(x- 3/2)^2- 11/2$. 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.