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.

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.

anonymous · Answer

@ganeshie8

anonymous · Answer

@Compassionate

anonymous · Answer

@iGreen

igreen · Answer

What's your birthday? Month and Day please.

anonymous · Answer

month: February  Day 7th

anonymous · Answer

@ganeshie8

anonymous · Answer

I figured out the answer to the first one 
@iGreen

anonymous · Answer

f(x)=3(x-2)^2+7

igreen · Answer

Lol you already have it, okay.

igreen · Answer

Standard form is: $ax^2 + bx + c$

anonymous · Answer

ok im gonna try to figure it out will post to make sure it's right i i think i have it

igreen · Answer

Okay.

anonymous · Answer

F(x)= 3x^2+12x-5

igreen · Answer

$f(x)=3(x-2)^2+7$

First get rid of the exponent:

$(x-2)^2 \rightarrow (x-2)(x-2)$

Multiply:

$x^2 - 2x - 2x + 4$

$x^2-4x + 4$

Now plug that back into the equation:

$f(x)=3(x^2-4x+4)+7$

Now distribute the 3 into the parenthesis:

$f(x)=3x^2-12x+12+7$

Add:

$f(x)=3x^2-12x+19$

igreen · Answer

You almost had it, the end is 19, not -5..I don't know how you made that mistake..

igreen · Answer

You probably subtracted 7 from 12 and made it negative.

igreen · Answer

So:

Vertex Form:

$f(x)=3(x-2)^2+7$

is the same thing as:

Standard Form:

$f(x)=3x^2−12x+19$

igreen · Answer

If you see those black diamond question marks, just click on a different post and go back to this one and it'll go back to normal.

anonymous · Answer

OK thanks for the help on that, Green. now i dont understand the last one

igreen · Answer

Here's the graph:

igreen · Answer

Okay, first let's find x = 4 and x = 7:

Plug x = 4 into the function and solve:

$f(x)=3(x-2)^2+7$

$f(x)=3(4-2)^2+7$

Can you solve that? @Rocketman27

igreen · Answer

$f(x)=3(4-2)^2+7$

Subtract:

$f(x)=3(2)^2+7$

Simplify exponent:

$f(x)=3(4)+7$

$f(x)=12+7$

Add:

$f(x) = 19$

So we have (4, 19).

igreen · Answer

Now let's solve for x = 7:

$f(x)=3(x-2)^2+7$

$f(x)=3(7-2)^2+7$

Subtract:

$f(x)=3(5)^2+7$

Simplify exponent:

$f(x)=3(25)+7$

Multiply:

$f(x)=75+7$

Add:

$f(x) = 82$

So we have (7, 82).

igreen · Answer

Now we have our two points, (4, 19) and (7, 82).

To find the average rate of change between them, plug them into the slope equation, $m = \dfrac{y_2-y_1}{x_2-x_1}$.

In this case:

$y_2 = 82$
$y_1 = 19$

$x_2 = 7$
$x_1 = 4$

Plug them in:

$m = \dfrac{y_2-y_1}{x_2-x_1}$

$m = \dfrac{82-19}{7-4}$

Subtract:

$m = \dfrac{63}{3}$

Divide:

$m = 21$

So the average rate of change between x = 4 and x = 7 is 21.

igreen · Answer

@Rocketman27

anonymous · Answer

Thank you. For the help @iGreen

igreen · Answer

No problem.