1. ## Help x-intercepts

1. What are the x-intercepts of y=(x−2)(x+5) ?

• A. (0, 2) and (0, -5)
• B. (0, -2) and (0, 5)
• C. (-2, 0) and (5, 0)
• D. (2, 0) and (-5, 0)

X-2=>
X=2 (2,0)

X+5=0
X=-5 (-5,0)

Correct or not

1. Which of these quadratic functions has exactly one x -intercept?

• A. y=x 2 −9
• B. y=x 2 −6x+9
• C. y=x 2 −5x+6
• D. y=x 2 +x−6

A

(X-#)(X+3)

CORRECT OR NOT

1. Which of the following parabolas opens upward and appears narrower than y=−3x 2 +2x−1 ?

• A. y= 4x 2 −2x−1
• B. y= −4x 2 +2x−1
• C. y= x 2 +4x

D. y= −2x 2 +x+

A

CORRECT OR NOT

THANKS MUCH

2. Originally Posted by yorkmanz
1. What are the x-intercepts of y=(x−2)(x+5) ?

• A. (0, 2) and (0, -5)
• B. (0, -2) and (0, 5)
• C. (-2, 0) and (5, 0)
• D. (2, 0) and (-5, 0)

X-2=>
X=2 (2,0)

X+5=0
X=-5 (-5,0)

Correct or not

1. Which of these quadratic functions has exactly one x -intercept?

• A. y=x 2 −9
• B. y=x 2 −6x+9
• C. y=x 2 −5x+6
• D. y=x 2 +x−6

A

(X-#)(X+3)

CORRECT OR NOT ...... Don't know - because the equations you posted above are not quadratic equations

1. Which of the following parabolas opens upward and appears narrower than y=−3x 2 +2x−1 ?

• A. y= 4x 2 −2x−1
• B. y= −4x 2 +2x−1
• C. y= x 2 +4x

D. y= −2x 2 +x+

A

CORRECT OR NOT..... Don't know - because the equations you posted above are not quadratic equations

THANKS MUCH
You are not posting correct problems.

As posted. you do not have a quadratic equation.

In your other post, I guessed the correct equation and posted it.

Now it is your turn - you will need to post correct problems.

3. Originally Posted by Subhotosh Khan
You are not posting correct problems.

As posted. you do not have a quadratic equation.

In your other post, I guessed the correct equation and posted it.

Now it is your turn - you will need to post correct problems.

1. Which of these quadratic functions has exactly one x -intercept?

• A. y=x^2 −9
• B. y=x^2−6x+9
• C. y=x^2 −5x+6
• D. y=x^2 +x−6

A

CORRECT OR NOT ...... Don't know - because the equations you posted above are not quadratic equations

2. Which of the following parabolas opens upward and appears narrower than y=−3x 2 +2x−1 ?

• A. y= 4x^2 −2x−1
• B. y= −4x^2 +2x−1
• C. y= x^2 +4x

D. y= −2x^2 +x+

A

CORRECT OR NOT..... Don't know - because the equations you posted above are not quadratic equations

THANKS

4. Originally Posted by yorkmanz
1. Which of these quadratic functions has exactly one x -intercept?

• A. y=x^2 −9
• B. y=x^2−6x+9
• C. y=x^2 −5x+6
• D. y=x^2 +x−6

A ............................ A has two x-intercepts x=3 and x=-3

CORRECT OR NOT ....Incorrect

2. Which of the following parabolas opens upward and appears narrower than y=−3x?2 +2x−1 ?.......?

• A. y= 4x^2 −2x−1
• B. y= −4x^2 +2x−1
• C. y= x^2 +4x

D. y= −2x^2 +x+ ? ............................................

A

CORRECT OR NOT..... Don't know

.

5. Originally Posted by yorkmanz
1. What are the x-intercepts of y=(x−2)(x+5) ?

• A. (0, 2) and (0, -5)
• B. (0, -2) and (0, 5)
• C. (-2, 0) and (5, 0)
• D. (2, 0) and (-5, 0)

X-2=>
X=2 (2,0)

X+5=0
X=-5 (-5,0)

Correct or not
Yes, that is correct. An "x- intercept" is a point on the graph where the graph crosses ("intersects") the x-axis. There y= 0. If y= (x- 2)(x+ 5)= 0 then either x- 2= 0 or x+ 5= 0. If x- 2= 0 then x= 2. If x+ 5= 0 then x= -5. In either case y= 0 so the x-intercepts are (2, 0) and (-5, 0).

1. Which of these quadratic functions has exactly one x -intercept?

• A. y=x 2 −9
• B. y=x 2 −6x+9
• C. y=x 2 −5x+6
• D. y=x 2 +x−6

A

(X-#)(X+3)

CORRECT OR NOT
No, that is not correct
A. $y= x^2- 9= (x- 3)(x+ 3)= 0$. We have either x- 3= 0 so x= -3 or x+ 3= 0 so x= -3. The two x-intercepts are (3, 0) and (-3, 0).
B. $y= x^2- 6x+ 9= (x- 3)^2= 0$. We must have x= 3. There is only one x-intercept.
C. $y= x^2- 5x+ 6= (x- 3)(x- 2)= 0$. We must have either x- 3= 0 so x= 3 or x- 2= 0 so x= 2. The two x-intercepts are (3, 0) and (2, 0).
D. $y= x^2+ x- 6= (x+ 3)(x- 2)= 0$. We must have either x+ 3= 0 so x= -3 or x- 2= 0 so x= 2. The two x-intercepts are (-3, 0) and (2, 0).

1. Which of the following parabolas opens upward and appears narrower than y=−3x 2 +2x−1 ?

• A. y= 4x 2 −2x−1
• B. y= −4x 2 +2x−1
• C. y= x 2 +4x

D. y= −2x 2 +x+

A

CORRECT OR NOT
Yes, that is correct.
A parabola opens upward if and only if its leading coefficient (the coefficient of $x^2$) is positive. That is true in A and C. How "narrow" a parabola appears depends upon how large the absolute value of the leading coefficient is. The larger the leading coefficient, the "narrower" the parabola is. |4|= 4 is larger than |-3|= 3 while |1|= 1 is not.

THANKS MUCH

6. Originally Posted by HallsofIvy
… An "x- intercept" is a point on the graph where the graph crosses ("intersects") the x-axis …
Rather than using "crosses the axis" or "intersects the axis", I prefer a phrase like "crosses or just touches the axis".

The word "crosses" (in particular) can imply for beginning students that curves always continue on the other side of the axis, which we know is not always the case.

7. Originally Posted by HallsofIvy
Yes, that is correct. An "x- intercept" is a point on the graph where the graph crosses ("intersects") the x-axis. There y= 0. If y= (x- 2)(x+ 5)= 0 then either x- 2= 0 or x+ 5= 0. If x- 2= 0 then x= 2. If x+ 5= 0 then x= -5. In either case y= 0 so the x-intercepts are (2, 0) and (-5, 0).

No, that is not correct
A. $y= x^2- 9= (x- 3)(x+ 3)= 0$. We have either x- 3= 0 so x= -3 or x+ 3= 0 so x= -3. The two x-intercepts are (3, 0) and (-3, 0).
B. $y= x^2- 6x+ 9= (x- 3)^2= 0$. We must have x= 3. There is only one x-intercept.
C. $y= x^2- 5x+ 6= (x- 3)(x- 2)= 0$. We must have either x- 3= 0 so x= 3 or x- 2= 0 so x= 2. The two x-intercepts are (3, 0) and (2, 0).
D. $y= x^2+ x- 6= (x+ 3)(x- 2)= 0$. We must have either x+ 3= 0 so x= -3 or x- 2= 0 so x= 2. The two x-intercepts are (-3, 0) and (2, 0).

Yes, that is correct.
A parabola opens upward if and only if its leading coefficient (the coefficient of $x^2$) is positive. That is true in A and C. How "narrow" a parabola appears depends upon how large the absolute value of the leading coefficient is. The larger the leading coefficient, the "narrower" the parabola is. |4|= 4 is larger than |-3|= 3 while |1|= 1 is not.

Thank you man .. that's a perfect explanation...

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