How do you solve y and x intercepts on: Y=2x to the 3rd -4x squared.. Please explain?

Question

I need it explained to me please someone help...Thank you so so much

Answer 1

I am almost absolutely sure I am right. I might be repeating some things you already know, so please feel free to skip those. The question is written as:

y = 2x^3 - 4x^2       '^' representing "to the power of"

The first and easiest thing to do would be to extract an "x^2" from the equation. Put it on the outside so that your equation looks something like:

y = (x^2)(2x - 4)     You notice the 2x missing an x^2 along with the 4)

When this is finished, you can commence with finding the intercepts. When you have a polynomial equation, the main way to find the x interecepts is to seperate it into monomials and binomials. That is your main objective. Your objective is to degenerate the polynomial into something easier to understand. If you degenerate it and it ends up a trinomial, then you degenerate that trinomial further into two binomials.

When you have your binomials or monomials, what you do next is equate those binomials/monomials to "0". So then your equation looks like:

y = x^2   and   y = 2^x - 4

When you're equating these two equations to zero, you are essentially placing a "0" in the place of your y's.

0 = x^2   and   0 = 2^x - 4

Then you solve your two equations. You square both sides of your first equation to get:

0 = x^2

square root (0) = square root (x^2)

x = 0

and then for your second equation:

0 = 2x - 4

4 = 2x

4/2 = x

2 = x

So now you have your x interecepts.

x = 2,0

As for your y interecept, in this type of equation, it is the constant. In order to find the y intercept, you take your equation and add a "0x + 0".

y = 2x^3 - 4x^2 + 0x + 0     The zeroes are being used as place

                                        holders for what could have been there.

                                        Since you don't know what could have been

                                        there, it's safe to say that the y-intercept is

                                        equal to zero.

So therefore,

x = 2,0

y = 0

Answer 2

To get the intercepts you simply plug in x=0 for the y-intercept, and y=0 for the x-intercept.

y = 2(x^3) - 4(x^2)

Y-intercept

y = 2(0) - 4(0) = 0

(0,0)

X-intercept

0 = 2(x^3) - 4(x^2)

2(x^3) = 4(x^2)

x = 2

(2,0)

Answer 3

Y INTERCEPT:

   set x to 0 to find where the graph crosses the y-axis

   so... y = 2(0)^3   -   4 (0)^2

          y  = 0 - 0

        y=0 ...          y intercept: (0,0)

X INTEREPT:

set y to 0 to find where the graph crosses the x-axis

    we already know one of the x intercepts is (0,0) because it crosses         both the x axis and y axis

so 0 = (2x)^3   -  (4x)^2

    0 =  8 (x^3)  -   16 (x^2) ....then factor 8 x squared out

   0  = { 8(x^2) } { x-2 }    .....then set each part equal to 0

0 =  8(x^2)    AND   0 = x-2

0 = x ^2        AND   2=x

x=0 ...so (0,0), which we already knew is a x-intercept

x = 2 ...so (2,0) is also an x intercept!

hope it is thorough enough ;) and at least clear!

Answer 4

Its been a while since I have done these.

y=2x3-4x2

y=-2x to the sixth.

I think that is right..not sure. What I think you do is when ever your variables match like x's and y's and you have exponents you multiply them and then just subtract the 2 from the 4 keeping the negative sign.