Question

How do i find the axis of symmetry of the equation y=a(X-5.68)^2+5.1

Answer 1

This equation is in Vertex form:
y=a(x-h)^2 + k

Do you know how to find the vertex from this equation? (vertex is the maximum of the parabola)

Answer 2

It is important to learn that the axis of symmetry lies on the vertex.
The axis of symmetry is represented by the equation x=?
Where x is the x coordinate of the vertex.

Answer 3

From the given equation, you can simply read this off as 5.68.
Be sure to include the correct sign though.
If the equation was (X+5.68), then the equation
for the axis of symmetry would be x= -5.86

Answer 4

Okay and how do i put that equation into y=ax^2+bx+C?

Answer 5

If i substitute x for 1

Answer 6

First you deal with the exponent which is the ^2. So now, using perfect squares expand.

Answer 7

??

Answer 8

Do you know what 'a' is?

Answer 9

No. Thats why im confused. What is "a" in the equation

Answer 10

Hang on, I think I know how to find it - im working on it.

'a' controls how skinny or fat the parabola/curve is.

Answer 11

Okay.

Answer 12

One of the ppints that the parabola pass through is (9,2) so i would have 2=a(9-5.68)^2+5.1?

Answer 13

To find a, you need a point (x,y) that lies on the equation. Has this been given to you? Is there any other information that you know?

Answer 14

Yep, you got it! :)

Answer 15

& i got -0.28?

Answer 16

I got:

2=a(9-5.68)62 +5.1
-3.1=a(3.32)^2
-3.1 = a11.0224
therefore, a = -3.1/11.0224
a=-0.281

Answer 17

Well done :)

Answer 18

okay. Me too so now how i do put that into the y=ax^2+bx+c thing

Answer 19

My equation is y=-0.28(x-5.68)^2+5.1

Answer 20

First step - expand (x-5.68)2 using perfect squares do you know how to do this?

Answer 21

No

Answer 22

ok hang on i'll write it out

Answer 23

Okay

Answer 24

im about to upload my working - wont take a sec

Answer 25

Do you have an answer?

Answer 26

Hold on

Answer 27

Am i solving for x?

Answer 28

Just to let you now that the vertex, which is your axis of symmetry can be easily found by nowing that the h = x and k = y in the equation \(a(x-h)^2 + k \)

You equation \( y=a(X-5.68)^2+5.1 \)
x = -5.68
y = 5.1

The vertex and your axis of symmetry = (-5.68, 5.1) That is your point and draw a line straight up and that will be your axis of symmetry

Answer 29

okay

Answer 30

No you are not solving for x - you are expanding into general form - isn't that what you asked?

Answer 31

Yes, i got the -0.28x^2+3.1808x-3.933

Answer 32

:)

Answer 33

Thats right?

Answer 34

Yes - i got the same as you :)

Answer 35

okay thanks alot!

Answer 36

One more question i have to find the discriminant ? How do i do that

Answer 37

Your welcome.

Answer 38

Okay, so do you know what the equation for the discriminant is?

Answer 39

No

Answer 40

it is\[\sqrt{b ^{2}-4ac}\]

Answer 41

Okay hold on

Answer 42

find a, b and c from the equation you just found (general form) and calculate

Answer 43

Okay so its the sqrt of 3.1808^2-4(-0.28)(3.933)?

Answer 44

I got that the discriminant equals 2.39...
Therefore since \[2.39>0\] then the quadratic has two distinct real roots
In other words, it cuts the x-axis twice

Answer 45

yes - everything is under the square root

Answer 46

i got 3.81

Answer 47

Yes you are right - just did it again sorry

Answer 48

So do i find the x-intercepts from that?

Answer 49

okay so its 3.81>0?

Answer 50

yes. 2.39>0
then the quadratic has two distinct real roots
In other words, it cuts the x-axis twice.

Does the question require you to find the x intercepts?

Answer 51

Yes

Answer 52

The x & y-intercepts

Answer 53

The discriminant does not tell you what the x - intercepts are,
it simply indicates if there are two roots (solutions), d\[\Delta \] which is the discriminant ,

if \[\Delta>0\]two solutions

if \[\Delta=0\]one solution

if \[\Delta<0\]no real roots (complex roots)

Answer 54

Anyway, to find the x intercept just let y=0

Answer 55

To find y intercepts, let x=0

Answer 56

And for the y?

Answer 57

okay hold on

Answer 58

So its 0=-0.28(x-5.68)^2+5.1? & y=-0.28(0-5.68)^2+5.1?

Answer 59

yep - just solve now

Answer 60

i got x intercepts are=9.95,1.41 & y intercepts are=-3.93

Answer 61

An x intercept should have co-ordinates (x,0) and y-in = (0,y)
try again

Answer 62

You should get two x intercepts, as indicated by the discriminant

Answer 63

so x ints are (1.41,0) and (9.95,0)
y int is at (0,-3.93)

you are correct

Answer 64

Yes thats what i got

Answer 65

:)