Question

use the function y=2x^2 -4x -6 to answer the following
a) show or explain how to find the axis of symmetry
b)show or explain how you would find the vertex.
c)show or explain how you would find the x-intercepts.
d) determine the y-intercept and explain how you would know what it is just from looking at the equation.
e) graph the function

Answer 1

@jaeuni

Answer 2

y intercept is -6 i think?

Answer 3

how are you at completing the square of the function is written as

\[y = 2(x^2 - 2x + ?) - 6\]

complete the square inside the brackets by adding ?

what do you need to add..?

Answer 4

wait a minute, you lost me?

Answer 5

do you know how to complete the square... its a method for solving quadratics..?

you want a perfect square inside the brackets

(x + a)^2 = x^2 + 2ax + a^2

Answer 6

or you need to get it to

(x -a)^2 = x^2 - 2ax + a^2

Answer 7

this is for step A? im really sorry, its hard for me to understand things :(

Answer 8

yes it is step A...

an easier option might be to use

\[x = \frac{-b}{2a}\]

this will give the line of symmetry and the x, value on the vertex

you have b = -4 and a = 2

so substitute them to find x...

Answer 9

b = 4 a = 6 right?

Answer 10

ok... just to get the letters right... the general form is

\[y = ax^2 + bx + c\]
so in your equation you have a = 2 and b = -4

Answer 11

ok y=2x^2+-4x+c

Answer 12

c = 6

Answer 13

ok... can you please stop...

Answer 14

Im really confused im sorry im doing no good here

Answer 15

the equation is

\[y = 2x^2 - 4x - 6\]

the line of symmetry is found using

\[x = \frac{-b}{2 \times a}\]

you have a = 2 and b = -4

can you use the formula to calculate the value of x, which is the line of symmetry

Answer 16

so you are calculating

\[x = \frac{-(-4)}{2 \times 2}\]

Answer 17

x=0 then, right?

Answer 18

-(-4) = 4
2*2 = 4
4/4 is 1

Answer 19

well you have \[x = \frac{4}{4} = 1\]

so the line of symmetry is x = 1

Answer 20

i meant 1 not 0

Answer 21

ok... so part A is done

Part B.

The vertex is in the line of symmetry so the point is (1, ??)

to find ?? just substitute x = 1 into the equation o find y

Answer 22

oops should read... the vertex is on the line of symmetry...

Answer 23

what do you get when you substitute x = 1 into the original equation..?

Answer 24

y= 2(1)^2 - 4(1) -6
y=2^2 - 4 -6
y=4 - 4 -6

Answer 25

well you substitute x = 1

so its

\[y = 2\times 1^2 - 4 \times 1 - 6\]

what's that value..?

Answer 26

yeah i had that but i was trying to simplify it, i guess i got ahead

Answer 27

you can type it into a calculator as its written

Answer 28

the value is -8

Answer 29

or is it -6?

Answer 30

great so that means the vertex is at (1, -8)

so to find the vertex, just substitute the value for the line of symmetry into the equation and solve for y.

Answer 31

now part C

let the equation = 0 to find the x intercepts

\[2x^2 - 4x - 6 = 0\]

divide every term by 2

\[x^2 - 2x - 3 = 0\]

are you able to factor this equation..?

Answer 32

what do you mean by able to factor it?

Answer 33

well can you write the equation as the product of 2 linear factors

as an example

\[a^2 - 8a - 20 =(a - 10)(a + 2)\]

Answer 34

ok earlier i factored 2x+6x+4 into 2(x+2)(x+1)

Answer 35

so you mean similar to that?

Answer 36

well its a start... yest... but there are a few errors in the factoring...

2 x -1 = -2 you need -3

adding them 2 + -1 = 1 you want -2...

so you need a little rethinking

Answer 37

of you factor out the 2 you get

\[2(x^2 - 2x - 3) = 0\]

Answer 38

ok so im trying to understand

Answer 39

so find the factors of -3 that add to -2 the larger factor is negative and the smaller factor is positive

Answer 40

ok hold on

Answer 41

when multiplied it needs to equal -3 but when added it needs to equal -2, right?

Answer 42

thats correct

Answer 43

-3 and positive 1

Answer 44

great so now you can write the equation as

\[2(x -3)(x+1) = 0\]

now if either of the linear factors x -3 or x + 1 equal zero, the whole thing will equal zero.

so you need to find the x values that make

x - 3 = 0 and x + 1 = 0


this will be where the parabola cuts the x-axis

Answer 45

3-3=0 and -1+1=0

Answer 46

great... so the x-intercepts are at (-1, 0) and (3, 0)

those points come from the solutions you just game me.

Now to Part D

this is probably the easiest... substitute x = 0 into the original equation to find y....

this will be the y-intercept.

Answer 47

any thoughts on the y-intercept..?

Answer 48

I know that it is -6 but do not know how to explain why

Answer 49

Y=2(0)^2 - 4(0) -6
Y= 4 - 4 - 6
Y= 6
So the y intercept is 6, right?

Answer 50

ok... well replace x with 0 and calculate

\[y = 2 \times 0^2 - 4 \times 0 - 6\]

so almost done...

now Part E

plot the points on the number plane

Vertex (1, -8)

x- intercepts (-1, 0) and (3, 0)

y- intercept (0, -6)

draw a line through all 4 points and you get a parabola.

you can use this site to check

https://www.desmos.com/calculator

hope it all helped.

Answer 51

Sorry I had to switch to the mobile app because my laptop died and it's all crazy. You've been a great help! And now finally I can go to bed! Thank you so much!! Can I tag you in a question tomorrow?