Question

Create a quadratic function, f(x), in vertex form. The a should be between 4 and –4, the h will be your birth month, and the k will be your birth day. Write your equation below.

Using complete sentences, explain how to convert your birthday function into standard form.

Graph your function. Include your graph below.

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

Answer 1

@phi

Answer 2

@iGreen

Answer 3

Please help me at least with first question

Answer 4

Quadratic form is: \(f(x) = ax^2 + bx + c\)

Answer 5

Wait..for here I think they're using:

\(y = a(x - h)^2 + k\)

Answer 6

Let's just pick 3 for a, since it wants it to be between 4 and -4.

Answer 7

\(y = 3(x - 4)^2 + 12\)

Answer 8

I believe that's it..

Is your birthday in April or December..? @carolina4567

Answer 9

Okay, so that's correct.

Your equation is: \(y = 3(x - 4)^2 + 12\).

Answer 10

So now we have to convert to standard form how would we do this ?

Answer 11

Yes.

Answer 12

standard form is
y = a x^2 + b x + c
where a, b and c are numbers

Answer 13

\(y = 3(x - 4)^2 + 12\)

Standard form = \(y = ax^2 + bx + c\)

\((a + b)^2 = a^2 + 2ab + b^2\)
\((x - 4)^2 = x^2 + 2x(-4) - 4^2\)
\((x - 4)^2 = x^2 - 8x- 16\)

So: \(y = 3(x^2 - 8x - 16) + 12\)

Distribute the 3:

\(y = 3x^2 - 24x - 48 + 12\)

Simplify:

\(y = 3x^2 - 24x - 36\)

Answer 14

Oh so thats how u do it now i get it

Answer 15

Ugh, I don't know how but I got the equation wrong. It's supposed to be \(y = 3x^2 - 24x + 60\)

Answer 16

Oh, I see it now.

Answer 17

\(y=3(x−4)^2+12\)

Standard form = \(y=ax^2+bx+c\)

\((a+b)^2=a^2+2ab+b^2\)
\((x−4)^2=x^2+2x(-4)+\color{red}4^2\)
\((x−4)^2=x^2−8x\color{red}+16\)

So: \(y=3(x^2−8x\color{red} +16)+12\)

Distribute the 3:

\(y=3x^2−24x\color{red} +48+12\)

Simplify:

\(y=3x^2−24x\color{red}{+60}\)

Answer 18

Okay, that's it.
If you see these: '�', then click on a different question and click back. It'll be normal.

Answer 19

Oh cool yea it looks fine now

Answer 20

Okay, that's it..

Answer 21

You can graph your equation here: https://www.desmos.com/calculator Just copy and paste your equation in one of the boxes on the left.

Answer 22

Be sure to put in the exponents.

Answer 23

Yes i did

Answer 24

Do you see the graph?

Answer 25

Yes

Answer 26

Okay, the formula for the average rate of change is \(m = \dfrac{y_2-y_1}{x_2-x_1}\). Your graph will tell you that when x is 4, y is 12.(4, 12) And when x is 7, y is approximately 39.

Answer 27

Okay so our points are:

\(y_2 \approx 39\)
\(y_1 = 12\)

\(x_2 = 7\)
\(x_1 = 4\)

Plug them in:

\(m \approx \dfrac{39-12}{7-4}\)

Subtract:

\(m \approx \dfrac{27}{3}\)

Divide:

\(m \approx 9\)

Remember, m is approximately 9, because 39 was approximate, and not exact.

Answer 28

Thank u so much for ur help @iGreen ur a life saver

Answer 29

No problem!