Is this quadratic function question wrong ?

[AhmedAlmosuli]

 

[Otis]

Is this quadratic function question wrong ?

Hi Ahmed. Yes, the exercise does not list the correct answer. I also get m+n+a=14.

I note that you've used a=2 below, to find a=8. That is another issue because a is constant.



I wish they would have used a different symbol for the y-coordinate in (-1,a) because the general form for quadratic polynomials is ax^2+bx+c. It's not good to use the same symbol for two different constants.

Your factorization is correct:

f(x) = 2(x – 3)(x)

If you expand the right-hand side, then you can confirm values for coefficients m and n. That will lead to f(-1)=8, too.

Here's yet another approach (it's how I started):

y = 2x^2 – mx + n

Substitute xy-coordinates from the three given points on the graph:

(0, 0) (3, 0) (-1, a)

Doing that yields a system of 3 equations to solve.
[imath]\;[/imath]

 

[Steven G]

Clearly your a is 2.
Now the function crosses (0,0). That makes n =0
The equation is now in the form of y=2x^2 - mx = x(2x - m) = 0 when x=0 and x=m/2 = 3. Hence m = 6
This tells us that y = 2x^2-6x. Now when x=-1, y = 8. That is, their a = 8

 

[AhmedAlmosuli]

Hi Ahmed. Yes, the exercise does not list the correct answer. I also get m+n+a=14.

I note that you've used a=2 below, to find a=8. That is another issue because a is constant.

View attachment 35178

I wish they would have used a different symbol for the y-coordinate in (-1,a) because the general form for quadratic polynomials is ax^2+bx+c. It's not good to use the same symbol for two different constants.

Your factorization is correct:

f(x) = 2(x – 3)(x)

If you expand the right-hand side, then you can confirm values for coefficients m and n. That will lead to f(-1)=8, too.

Here's yet another approach (it's how I started):

y = 2x^2 – mx + n

Substitute xy-coordinates from the three given points on the graph:

(0, 0) (3, 0) (-1, a)

Doing that yields a system of 3 equations to solve.
[imath]\;[/imath]

Thanks for your help ??

 

[AhmedAlmosuli]

Clearly your a is 2.
Now the function crosses (0,0). That makes n =0
The equation is now in the form of y=2x^2 - mx = x(2x - m) = 0 when x=0 and x=m/2 = 3. Hence m = 6
This tells us that y = 2x^2-6x. Now when x=-1, y = 8. That is, their a = 8

Thanks for your help ??