Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function and rank the functions based on their axis of symmetry (from smallest to largest).

Answer 1

f(x) = −2(x − 4)2 + 2
g(x) = 5x2 − 10x + 7
h(x)=

Answer 2

@esamalaa

Answer 3

Dee:
May I ask you to please find the formula for "axis of symmetry." Hint: It's part of the quadratic formula. If you don't already know this formula, why not do an Internet search for "axis of symmetry"?

Once you've typed in that formula here, I'd be h appy to continue working with you towards finding a solution to this problem.

Answer 4

I saw you were typing a response, but then stopped. ??

Answer 5

x=-b/2a

Answer 6

Great.

Now you're given 3 quadratics, A, B and C (C is just a graph).

Can you re-write f(x) = −2(x − 4)2 + 2 so that it's in standard form,
y = ax^2 + bx + c?

can y ou determine a, b and c for g(x) = 5x2 − 10x + 7?

Can you identify the coordinates of the vertex of the parabola in C?

Answer 7

thats my problem..

Answer 8

Try "can y ou determine a, b and c for g(x) = 5x2 − 10x + 7?" first. This equation is already in standard form, so you just need to pick out the coefficients which represent the values of a, b and c.

Answer 9

5x2 (a) 10x (b) 7 (c)?

Answer 10

can y ou determine a, b and c for g(x) = 5x2 − 10x + 7?

Match up the coefficients as follows:

5x2 − 10x + 7
ax^2 + bx + c

Comparing the coeff. of the x^2 term, a=5. What are b and c? Be careful with the signs.

Answer 11

-10 & 7

Answer 12

Right. So, if x=-b?(2a) is the equation for finding the x-coordinate of the vertex, and a= 5, b=-10 and c= 7, please identify the x -coord of the vertex for this particular situation.

Answer 13

x=100

Answer 14

But wouldn't -b/(2a) be -(-10)/(2*5)? = to what?

Answer 15

ohhhhh i was multiplying so 1?

Answer 16

Yes, as 10/10 = 1. So, the x-coordinate of the vertex of the 2nd parabola is
x=1.

Now look at the graph that represents parabola C. What is the x-coord of the vertex there?

Answer 17

wait so f(x) is 1 also ?

Answer 18

No, sorry. Please, let's take care of the third parabola first; please lok at the graph carefully, find the vertex, and determine what the x-coord. of the vertex is. It's not 1.

Answer 19

-3.5?

Answer 20

-2. my bad!

Answer 21

Think of the vertex as being teh very tip of your nose. Instead of seeing -3.5, I see the vertex x-ccord. as being x=-2. yes.

Answer 22

(thinking)

Answer 23

We're now done with B and C.
What about A?

A is not a quadratic in std. form. We must muliply, add and subtract to put it into standard form, ax^2 + bx + c.

Answer 24

I'd like to see where you're coming from in terms of understanding this.
What would you do first to put f(x) = −2(x − 4)2 + 2 into standard form?

Answer 25

distribute?

Answer 26

Well, yes, but first, please notice that you have the square of a binomial in there. Looking carefullyl, I've seen that you have (x-4)^2. That ^2 represents an exponent of 2.

Answer 27

Please go ahead: expand (x-4)^2. We'll deal with the other terms later.

Answer 28

x^2-8 ?

Answer 29

did you apply the FOIL method of expanding the square of a binomial? Your result should have 3 terms; currently it has only 2. What went wrong?

Answer 30

Note that (x-4)^2 is represented by (x-4)(x-4).

Which ever is easier for you, please multiply that or (x-4)^2 out.

Answer 31

(x-4)(x-4)=x^2-8x+16

Answer 32

That's good. I'd suggest y ou write that down as a reminder of how to do this sort of problem in the future.

Answer 33

okay!

Answer 34

f(x) = −2(x − 4)2 + 2 then becomes -2(x^2-8x+16)+2.
Would you do the indicated multiplication and then simplify the result to obtain this equation in std. form, please.

Answer 35

-2x^2+16x-30

Answer 36

Great! {please review that process, as you're likely to have to do it again.
Now, remembering that

x=-b/(2a),

please find the x-coord of the vertex for parabola A.

x=?

Answer 37

-2(A) 16(B) -30(C)

Answer 38

Yes (although I'd much prefer you write them as a=-2, b=16, c=-30).

Answer 39

thus, x= ??

Answer 40

4?

Answer 41

Very good.

Answer 42

Now, please write your x-coordinates for A, B and C here.

For A it's x=4; for B, it's x = ? and for C, it's x= ???.

Just go back and fetch these values from our previous discussion.

Answer 43

b=1 c=-2

Answer 44

Good; now, please arrange these 3 x-coordinates in ASCENDING order.

Answer 45

c=-2 b=1 a=4

Answer 46

right?

Answer 47

Except for a little house-cleaning, that's a great answer.

You might write, "The x-coodinates of the 3 vertices, arranged in ascending order, are -2, 1 and 4, corresponding to parabolas C, B and A."

Answer 48

so, you're done now, and done well.

Answer 49

Are u OK with this discussion? Did it answer all of your questions and concerns?

Answer 50

Surely enjoyed working with you! All the best to you. MM

Answer 51

help me with "Roy exclaims that his quadratic with a discriminant of −9 has no real solutions. Roy then puts down his pencil and refuses to do any more work. Create an equation with a negative discriminant. Then explain to Roy, in calm and complete sentences, how to find the solutions, even though they are not real." please?