Question

How do I put y=-5x^2-40x-6 in intercept form

Answer 1

can it be divided into 2 equations? Because that is the only possible way that this equation is making sense to me

Answer 2

I think so

Answer 3

yeah this question seems easy but is actually not

Answer 4

Hi!
what is "intercept form"?

Answer 5

y=mx+b
she/he meant slope intercept form

Answer 6

lol no

Answer 7

it is not a line, so it will not look like \(y=mx+b\)

Answer 8

lol yeah well i came here to answer because it appeared easy and now I want to know how you solve so yeah... if you know how then explain please :)

Answer 9

maybe it means "factor"

Answer 10

but this one does not factor with integers, so who knows?

Answer 11

yeah I tried to divide it into (x-a)(x-b)=c but it didnt gave an answer either

Answer 12

Slope intercept form only applies to straight lines.\[y=-5x^2-40x-6\]is not a straight line, and so it can't be represented using slope intercept form.

Answer 13

You can factor\[y=-5x^2-40x-6\]to become:\[y=-(5x^2+40x+6)=-(5x+40x+6)=-[(5x+0)(x+8)+6]=-(5x+0)(x+8)-6\]

Answer 14

@mathmate

Answer 15

For a quadratic, intercept form means
f(x)=a(x-p)(x-p) where p, q are the roots of the function.

As @misty1212 pointed out, this one does not have rational factors, so it is less obvious.

Answer 16

To work out this problem, we need to solve the quadratic and find the two irrational roots p,q.
Using the quadratic formula for
f(x)=\(-5x^2-40x-6\)
a=-5,
b=-40
c=-6
x=\(\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)
=\(\dfrac{40\pm\sqrt{40^2-4(-5)(-6)}}{2(-5)}\)
=\(\dfrac{20\pm\sqrt{370}}{5}\)
Putting the roots into the intercept form gives
f(x)=\(-\dfrac{1}{5}(5x+(\sqrt{370}+20))(5x-(\sqrt{370}-20))\)
which is the final intercept form.
You should always expand the form to confirm that it is indeed
f(x)=\(-5x^2-40x-6\)
I will leave that to you as part of the exercise.

I have exceptionally provided the final answer, partly because the arithmetic is tedious, and partly because I suspect there is a typo in the question. So whenever we come to a result like this, it is always a good idea to double check the question, in exams as well as in exercises.