MATHEMATICS MIDDLE SCHOOL

Quadratic graphs:y = x2 + 4x + 1

I need to work out the coordinates.
Help.

Answers

Answer 1

Answer: if x =1,
y= 1^2 +4(1) +1
=7
x=0, y=1

Answer 2

Answer:

Answer:

Basically what you have to do to draw the graph is creating a bunch of points that are part of the equation

to do so, you assign different values to x and find the corresponding y

for example

x=0 0^2 +4*0 +1 = 1 therefore y = 1

x=1 1^2+4*1 +1 = 6 therefore y= 6

and so on....

x=-1 y=-2

and as many as you need

this is valid...only if I have understood your question :-)

Step-by-step explanation:

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an animal shelter in a 36 kittens and 12 puppies available for adoption what is the ratio of puppies to kittens

Answers

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3 times as much as the sum of 3-4 and 2-6.

Answers

¹³/₄ or 3¹/₄ or 3.25

Further explanation

The Problem:

3 times as much as the sum of $(3)/(4)$ and $(2)/(6)$
Write an expression to match, and then solve.

The Process:

Here are some early expressions that need attention.

three-quarter is $\boxed{(3)/(4)}$
two-sixth is $\boxed{(2)/(6)}$
the sum of $(3)/(4) \ and \ (2)/(6)$ is $\boxed{(3)/(4) + (2)/(6)}$

Let us write an expression to match for3 times as much as the sum of $(3)/(4)$ and $(2)/(6)$

$\boxed{\boxed{ \ 3 * \bigg((3)/(4) + (2)/(6) \bigg) \ }}$

Let us calculate the operation in parentheses at first.

$(3)/(4) + (2)/(6)$

A least common multiple of 4 and 6 is 12. We use to equate the denominator.

$(3 * 3)/(4 * 3) + (2 * 2)/(6 * 2)$

$(9)/(12) + (4)/(12)$

$(13)/(12)$

And now we solve the full expression.

$\boxed{ \ = 3 * \bigg((3)/(4) + (2)/(6) \bigg) \ }$

$\boxed{ \ = 3 * (13)/(12) \ }$

We cross out 3 and 12 because they both can be divided.

$\boxed{ \ = 1 * 1(13)/(4) \ }$

$\boxed{\boxed{ \ = (13)/(4) \ }}$

In mixed fraction:

$\boxed{ \ (13)/(4) = \ ? \ }$

$\boxed{ \ = (12)/(4) + (1)/(4) \ }$

$\boxed{ \ = 3 + (1)/(4) \ }$

$\boxed{\boxed{ \ = 3(1)/(4) \ }}$

In decimal:

$\boxed{ \ 3(1)/(4) = \ ? \ }$

$\boxed{ \ = 3(1 * 25)/(4 * 25) \ }$

$\boxed{ \ = 3(25)/(100) \ }$

$\boxed{\boxed{ \ = 3.25 \ }}$

$\boxed{\boxed{ \ Thus, \ the \ result \ is \ (13)/(4) \ or \ 3(1)/(4) \ or \ 3.25 \ }}$

- - - - - - - - - -

Quick Steps:

Simplify $\boxed{(2)/(6) = (1)/(3)}$

$\boxed{ \ = 3 * \bigg((3)/(4) + (2)/(6) \bigg) \ }$

$\boxed{ \ = 3 * \bigg((3)/(4) + (1)/(3) \bigg) \ }$

$\boxed{ \ = 3 * \bigg((3 * 3)/(4 * 3) + (1 * 4)/(3 * 4) \bigg) \ }$

$\boxed{ \ = 3 * \bigg((9)/(12) + (4)/(12) \bigg) \ }$

$\boxed{ \ = 3 * (13)/(12) \ }$

$\boxed{\boxed{ \ = (13)/(4) \ }}$

$\boxed{\boxed{ \ = 3(1)/(4) \ }}$

$\boxed{\boxed{ \ = 3.25 \ }}$

Learn more

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Keywords: 3 times, as much as, the sum of 3/4 and 2/6, write an expression to match, and then solve, the result, in mixed fraction, decimal, ¹³/₄ or 3¹/₄ or 3.25

2 - 3 = -1 2 - 6 = -4 -4 + -1 = -5 -5 x 3 = ?

Simplify the expressions:

3x-1/3x+1

Answers