Question

help thanks. picture added.

Answer 1

For question 18, you need to remember what the formula for the discriminant is.
\[b ^{2}-4ac\] So in the given equation plug in your values for a, b, and c
a= k+1
b=2k
c=3k

Answer 2

yep, i did that but there was no answer for it.

Answer 3

b^2-4ac
=(2k)^2-4(k+1)+3k
=4k^2 -4k -4 + 3k
=4k^2-k-4
there is no answer i can select from the answers given above.

Answer 4

Here are the steps.\[(2k)^{2}-[4(3k)(k+1)]\] \[4k ^{2} -[12k ^{2}+12k]\] Now make sure to distribute the negative to get the following\[-8k ^{2}-12k\]

Answer 5

kk got it, i forgot to times a & c together, thanks!

Answer 6

Your setup is incorrect because you need to multiply 4 times a times c

Answer 7

yes there you go.

Answer 8

can u help me with question 20 as well?

Answer 9

I would just use guess and check for 20. Plug each answer in for m and use your calculator to check the intersections.

Answer 10

but is that the only way of solving it? because if a similar question were to be on my test then i wouldn't really have that much time.

Answer 11

However if you have to show your work:
In order for a line to only intersect a parabola once it would have to intersect at the vertex. So find the vertex and it will be a point on that line. Your parabolas equation\[y=x ^{2}+4\] gives the vertex (0, 4) therefore the point of intersection would be (0, 4).
Now use the linear equation\[y=2x+m\] and plug in your point values to solve for m.

Answer 12

Does that make sense?

Answer 13

yep it makes sense but i get the wrong answer from doing that.

Answer 14

Sorry I had a brain fart there, it does not have to intersect at the vertex...because the correct answer actually intersects the parabola at about (1,5)

Answer 15

where & how did u get (1,5) from?

Answer 16

I put the equations in my graphing calc and found the intersection

Answer 17

hmm but i'm sure there is some way of solving it manually, i just know it but can't seem to find how to do it.

Answer 18

and i don't think i can plot the y=2x + m because there is 3 unknowns?

Answer 19

Are you not allowed to use the calculator on your test? Because it is actually much faster to use the calc..

Answer 20

No you cannot plot 2x+m

Answer 21

Are you in a calculus course?
Because the manual way requires some knowledge of derivatives....

Answer 22

so i plot y=2x+4 right? from the vertex or turning point u told me (0,4). and yes for this next test i am allowed calculator but it's a combination of all quadratics, cubics and quartics so yeh.

Answer 23

well i live in australia so yeh, i'm not too sure but i'm still in high school and the maths i do is called "Maths Methods" and it does contain some calculus?

Answer 24

No what i mean is to test the values in your calc. You can plug in all of the lines at once. look at the attached pic

Answer 25

wow, ur calculator seems so much easier. At my school we use the Casio Classpad so yeh it's a bit different.