What intercepts to state..

[12345678]

‘Sketch the curve Y = (5 – 8X - X²)(X + 4), giving the coordinates of the points where the curve crosses the coordinate axes’ (5 marks)
X + 4 = 0
X = -4, so the x intercept is ( -4, 0)
Y intercept @ x=0 = (5 – 8(0) – 0²)(0 + 4) = 5 * 4 =20
Y intercept = (0 , 20)
My question is;
As the graph is a cubic, it has more intercepts
In the previous question I solved Y = 5 – 8X - X² giving X = -4 +- √21 --- Why do I not plot the intercepts of X = -4 - √21 and -4 + √21.. ??
The mark scheme only asks for (-4,0) and (0,20)

 

[lookagain]

‘Sketch the curve Y = (5 – 8X - X²)(X + 4),
giving the coordinates of the points where the curve crosses the coordinate axes’ (5 marks)
X + 4 = 0
X = -4, so the x intercept is ( -4, 0)
Y intercept @ x=0 = (5 – 8(0) – 0²)(0 + 4) = 5 * 4 =20
Y intercept = (0 , 20)

My question is;
As the graph is a cubic, it has more [x-]intercepts \(\displaystyle \ \ \ \) No, that is not necessarily true. It *is* true for this one.

In the previous question I solved Y = 5 – 8X - X² giving X = -4 +- √(21) ---

Why do I not plot the intercepts of X = -4 - √(21) and -4 + √(21).. ?? ***
\(\displaystyle \ \ \ \ \) You would unless the question places restrictions on the x-intercepts,
or the person who programmed the answers made an error of omission, for example.

The mark scheme only asks for (-4,0) and (0,20)

Those are indeed y intercepts as is clearly evident from \(\displaystyle \ \ \ \ \) **They are x-intercepts.**

\(\displaystyle Y[-4\pm\sqrt{21}]=0\)

Maybe you all haven't reached quadratic equations yet and you aren't expected to know how to find
the zeros of the quadratic term on the left.

Anyway, well done, your X values above are indeed > > > y axis intercepts < < < for your function Y above.

*** The x-values above are the x-coordinates of the x-axis intercepts.

 

[12345678]

Thanks all- it was on the official mark scheme so its pretty strange