Question

how do i graph g(x)=-2(x-1)^2+7

given this, i know that the vertex is (1,7)
how do i find the x intercepts?

Answer 1

set g(x)=0

Answer 2

then i use the quadratic formula?

Answer 3

yes, but you don't have to go that far, you can just subtract 7 from each side, divide by -2 on each side, and take square root of each side

Answer 4

remember when you square root on each side you have a positive and negative

Answer 5

do i have to expand the (x-1)^2?

Answer 6

so it would look like -2x^2-2x+8

Answer 7

you don't have to if you do it the way i suggested. it's up to you if you're more comfortable using the quadratic formula

Answer 8

if you expanded you would have:
-2(x^2-2x+1)+7=
-2x^2+4x-2+7=
-2x^2+4x+5

Answer 9

so from where u left off i could use the quadratic formula

Answer 10

yes

Answer 11

im curious about the method that u earlier mentioned, would i get the same results as to using quadratic formula?

Answer 12

yes

Answer 13

you solve like a regular algebra problem

Answer 14

and i can use that for all equations!? :O

Answer 15

does "completing the square" sound familiar?

Answer 16

yeah my teacher told me thats how we find the vertex

Answer 17

but we already found the vertex since its given in the equation here

Answer 18

yes, there are a couple ways to find vertex. u can also easily find vertex when problem is in form ax^2+bx+c, the vertex is at (-b/(2a),f(-b/(2a)))

Answer 19

im getting something really weird when i punch it into the quadratic formula

Answer 20

you will get irrational zeros

Answer 21

the heck, how do i graph it then? @_@

Answer 22

\[x=\frac{2 \pm \sqrt{14}}{2}\]

Answer 23

use a calculator to get decimal approximation

Answer 24

x=-0.87 or x=2.87

Answer 25

oh yeah! and for this the answer you got above did u factor out the 2 or something?

Answer 26

yes, i factored

Answer 27

how did u factor it when there's a +5?

Answer 28

-2x^2+4x+5

-2(x^2+2x) + 5?

Answer 29

f(x)=-2x^2+4x+5
\[x=\frac{-4 \pm \sqrt{16-4(-2)(5)}}{2(-2)}\]
\[x=\frac{-4 \pm \sqrt{56}}{-4}=\frac{-4 \pm \sqrt{14*4}}{-4}=\frac{-4 \pm 2\sqrt{14}}{-4}=\frac{-2 \pm \sqrt{14}}{-2}=\frac{2 \pm \sqrt{14}}{2}\]

Answer 30

thank you very much appreciated your assistance, again

Answer 31

you're welcome