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3 years ago

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You have worked with three forms of quadratic functions. Think about them and answer the following questions in complete sentenc

es.
1) What are the different forms?

2) For each of the three forms, when would it be most convenient to have the function in that form?

3) Create a quadratic function in one of the forms and show how to convert it to another one of the three forms.

Number your responses from 1 to 3.

2 answers:

ludmilkaskok [199]3 years ago

8 0

Step-by-step explanation:

1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.

2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.

3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.

Angelina_Jolie [31]3 years ago

5 0

Answer:

1. standard form, factored form, vortex form

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A 3 ounce serving of tuna provides 21 grams of protein. Use equivalent ratios to find how many grams of protein are in 9 ounces

denis-greek [22]

Answer:

There would be 63 grams of protein in 9 ounces of tuna.

Step-by-step explanation:

Equivalent ratios compare two different quantities the have the same rate regardless of the amount. In this example, for every 3 ounces of tuna, there are 21 grams of protein. We can write this as a ratio of: 3/21. Like fractions, we can simplify ratios by dividing the numerator and denominator by the same greatest common factor. In this case, we would divide both the numerator and denominator by 3: (3÷3)/(21÷3) = 1/7. So, our new ratio is for every ounce of tuna, we have 7 grams of protein. Using equivalent ratios, we can set up our ratios to solve for the grams of protein in 9 ounces of tuna: 1/7 = 9/x. Since we have to multiply both the numerator and denominator by the same factor, in this case 9, then our x = 63 grams of protein.

5 0

3 years ago

No Solutions<br> 5x - 2x + 7 - x = _x + _

Eddi Din [679]

Answer:

2x+7

Step-by-step explanation:

To Simplify an Expression , we combine Like-Terms

So for our Question , we have Terms with x and Constant Term

Combine Terms with x : 5x-2x-x=2x

Constant Term : 7

Then 5x-2x+7-x = 2x+7

5 0

2 years ago

Read 2 more answers

Eleanor recently visited a bank to get a car loan. Upon reviewing her credit score, the bank decided to deny her request for a c

xenn [34]

Answer:

victim of identity theft and credit report

Step-by-step explanation:

got it right on my test

8 0

4 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

Not the best pic but I think it’s still readable.. pls answer for all.. thanks

luda_lava [24]

Answer:

a) y=5ˣ-3

b) y=5ˣ⁻²

c) y=5^(x+1/2)

d) y=5^(x+2.5)+1

Step-by-step explanation:

$y=b*5^{ax-h}+k$

b: vertical stretch or compression and reflection across x-axis

a: horizontal stretch or compression and reflection across y-axis

h: horizontal shift (left and right)

k: vertical shift (up and down)

a) y=5ˣ-3

b) y=5ˣ⁻²

c) y=5^(x+1/2)

d) y=5^(x+2.5)+1

5 0

3 years ago