Question

algebraically find the x-intercept(s) of this quadratic relation y= -x^2+2x+8

Answer 1

Could I help you?

Answer 2

You have to factor this quadratic, putting it into intercept form.

Answer 3

@confuzion

Answer 4

How would i do that

Answer 5

"find the x-intercept(s) of this quadratic relation" means where does this parabola strike/intersect/touch the x-axis.

In other words, it wants the roots (the solution) of this quadratic equation!

Answer 6

I know the xintercepts are -2 and 4 but how do i algebraically find that out

Answer 7

Use the quadratic formula to find out these two, or as @ShadowLegendX
has said; factor this quadratic!

Answer 8

\[y= -x^2+2x+8 \]

Factor out -1

\[y= -(x^2 -2x-8)\]

The product of 2 and -4 is -8
The sum of -4 and 2, is -2

\[y = -(x - 4)(x + 2)\]

Answer 9

Take the opposite sign of -4 and 2,

Roots are 4 and -2

Answer 10

so i don't do anything with the negative sign in front of the brackets

Answer 11

In the future, if you end up with parentheses that have something like

(2x -5)(3x + 2)

Solve for the roots by equaling them to zero, like so

2x - 5 =0
2x = 5
x = 5/2

3x + 2 = 0
3x = -2
x = -2/3

Answer 12

No, they just wanted the roots

Answer 13

or the "x-intercepts"

Answer 14

okay thanks

Answer 15

Since they ask for the algebraic method, I would show your work how you got those roots

x - 4 = 0
x = 4

x + 2 = 0
x = -2

Answer 16

\[\LARGE {y = -(x - 4)(x + 2)\\let~~ y=0\\-(x - 4)(x + 2)=0\\(x - 4)(x + 2)=0\\(x-4)=0~~~or~~~(x+2)=0\\x=4~~~~~~and ~~~~~~~x=-2}\]

Answer 17

@ShadowLegendX AND @3mar Thanks

Answer 18

Don't mention it!
That is with my pleasure!
Any Help... Any Time...


Any more questions?

Answer 19

No but thank you so much!

Answer 20

Don't hesitate to ask me if there is any difficulty faces you!

Answer 21

@confuzion the reason the negative sign in front of the factors doesn't matter is that you can pass an infinite variety of parabolas through a given pair of x-intercepts. Try graphing the following:

\[y=-(x-1)(x+1)\]\[y=-2(x-1)(x+1)\]\[y=3(x-1)(x+1)\]on the same graph. You can do this by giving google the following search string:

plot -1(x-1)(x+1), -2(x-1)(x+1), 3(x-1)(x+1)