Question

what is the equation of the line symmetry for f(x)=2x2-12x-20?

Answer 1

for \[y=ax^2+bx+c\]use \[x=-\frac{b}{2a}\]

Answer 2

Simplify 2x^2 - 12x

Answer 3

Equation becomes (2x^2 - 12x) - 20 = 0

Answer 4

Simplify 2x^2-12x - 20

Answer 5

So, simplify the equation

Answer 6

Pull out like factors :

Answer 7

2x^2 - 12x - 20 = 2 • (x^2 - 6x - 10)

Answer 8

Factoring x^2 - 6x - 10

Answer 9

The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is -10

Answer 10

Multiply the coefficient of the first term by the constant 1 • -10 = -10

Answer 11

Find two factors of -10 whose sum equals the coefficient of the middle term, which is -6 .

Answer 12

oh okay

Answer 13

-10 + 1 = -9
-5 + 2 = -3
-2 + 5 = 3
-1 + 10 = 9

Answer 14

2 • (x^2 - 6x - 10) = 0

Answer 15

Solve 2•(x^2-6x-10) = 0

Answer 16

Solve : 2 = 0

Answer 17

Is that true or false?

Answer 18

I know that 2 does not equal 0

Answer 19

Ok so is it true or false?

Answer 20

false

Answer 21

If true than it has a solution if not than no solutions.

Answer 22

This equation has no solution.
A a non-zero constant never equals zero.

Answer 23

yep, it does not

Answer 24

Do you need the vertex as well?

Answer 25

well, sure if you want to

Answer 26

Not sure what you're doing here, but this question doesn't ask for solutions to the quadratic. It asks for the line of symmetry, in other words the vertical line that passes through the vertex. @satellite73 showed you how to do it in the first reply to this post.

Answer 27

oh yea, that's what i was about to say

Answer 28

Ok so from here we will find the vertex

Answer 29

The vertex of the parabola relates to its axis of symmetry and how to determine the axis of symmetry from a quadratic equation.

Answer 30

Find the Vertex of y = x^2-6x-10

Answer 31

i'm trying to get question done, cuz i'm on my quiz, and i don't it want it to take long

Answer 32

Parabolas have a highest or a lowest point called the Vertex .

Answer 33

Ok well I was showing you how I do it but my way is different from others. We will end up at the same end point.

Answer 34

You don't need solutions, you don't need the coordinates of the vertex. To answer the question, compare the given quadratic to \[y=ax^2 + bx + c\]Determine the values os a, b, and c. The equation of the line of symmetry is then\[x=-\frac{ b }{ 2a }\]

Answer 35

okay so 2x2 is a, -12 is b and -20 is c?

Answer 36

-12x i met for b

Answer 37

a=2, b=-12, c=-20

Answer 38

@ospreytriple we will end up with the same answer I just do it differently.

Answer 39

okay, so i think my answer is -3

Answer 40

There's an issue with the sign. Check your work again very carefully.

Answer 41

\[x=-\frac{ b }{ 2a } = -\frac{ -12 }{ 2(2) }\]

Answer 42

oh

Answer 43

What do you get?

Answer 44

oh wait it's +3 is it?

Answer 45

Right. But you have yo write the full equation of the line, i.e. \(x=3\)

Answer 46

oh x=3 got it

Answer 47

Good job.

Answer 48

well, thank you very much, and other two help me good too