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3 years ago

Find the y-intercept of the parabola y=x^2

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

6 0

Hello!

The y intercept of the parabola is when one of it's function's hits/intersects the y axis. The y intercept of the parabola y = x^2 is (0,0).

You may be wondering where is that, and why is it there. Y = x^2 is a parent function.

Check the image below for better explanation from me.

(0,0) = y - intercept

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Please Help!!

Genrish500 [490]

Given

$a\sqrt{x+b}+c=d$

we have

$\sqrt{x+b}=\dfrac{d-c}{a}$

Squaring both sides, we have

$x+b=\dfrac{(d-c)^2}{a^2}$

And finally

$x=\dfrac{(d-c)^2}{a^2}-b$

Note that, when we square both sides, we have to assume that

$\dfrac{d-c}{a}>0$

because we're assuming that this fraction equals a square root, which is positive.

So, if that fraction is positive you'll actually have roots: choose

$a=1,\ b=0,\ c=2,\ d=6$

and you'll have

$\sqrt{x}+2=6 \iff \sqrt{x}=4 \iff x=16$

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

$a=1,\ b=0,\ c=10,\ d=4$

and you'll have

$\sqrt{x}+10=4 \iff \sqrt{x}=-6$

Squaring both sides (and here's the mistake!!) you'd have

$x=36$

which is not a solution for the equation, if we plug it in we have

$\sqrt{x}+10=4 \implies \sqrt{36}+10=4 \implies 6+10=4$

Which is clearly false

7 0

3 years ago

Marla bought 12 books at a garage sale. Some of them were hardback and the rest were paperback. She paid $0.50 for each paperbac

olga nikolaevna [1]

Answer: The number of books bought were 9 paperbacks and 3 hardbacks

Step-by-step explanation: We shall start by assigning letters to the unknown variables, hence let the hardback be called h, while the paperback shall be called p.

If Marla bought 12 books at the garage sale, that means she bought

h + p = 12 ------(1)

Then she paid 0.5 dollars for paperback and 0.75 dollars for hardback and the total spent was 6.75 dollars for all of them, then we can express these as follows;

0.5p + 0.75h = 6.75 ------(2)

We now have a pair of simultaneous equations which are

h + p = 12 ------(1)

0.5p + 0.75h = 6.75 ------(2)

From equation (1), make h the subject of the equation,

h = 12- p

Substitute for h into equation (2)

0.5p + 0.75(12 - p) = 6.75

0.5p + 9 - 0.75p = 6.75

0.5p - 0.75p = 6.75 - 9

-0.25p = -2.25

Divide both sides of the equation by -0.25

p = 9

Now, substitute for p into equation (1)

h + p = 12

h + 9 = 12

Subtract 9 from both sides of the equation

h = 3

Therefore Marla bought 9 paperbacks and 3 hardbacks

6 0

3 years ago

Read 2 more answers

Divide <br><br> (3x^2 + 9x + 7) divide by (x+2)

scZoUnD [109]

Answer:

The remainder is: 3x+3

The quotient is: 1

Step-by-step explanation:

We need to divide

(3x^2 + 9x + 7) by (x+2)

The remainder is: 3x+3

The quotient is: 1

The solution is attached in the figure below.

3 0

3 years ago

Read 2 more answers

Tell whether the table of values represents a

spin [16.1K]

Exponential Function.

Plotting the graph using this table gives the first figure. An exponential function has this kind of graph.

4 0

2 years ago

What’s the gcf of 18k and 15k cubed?

Contact [7]

Answer:

The GCF for the variable part is

Step-by-step explanation:

Since

contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.

Steps to find the GCF for

1. Find the GCF for the numerical part

2. Find the GCF for the variable part

3. Multiply the values together

Find the common factors for the numerical part:

The factors for

are

Tap for more steps...

The factors for

are

Tap for more steps...

List all the factors for

to find the common factors.

The common factors for

are

The GCF for the numerical part is

GCF

Numerical

Next, find the common factors for the variable part:

The factor for

itself.

The factors for

are

⋅

List all the factors for

to find the common factors.

⋅

The common factor for the variables

The GCF for the variable part is

GCF

Variable

Multiply the GCF of the numerical part

and the GCF of the variable part

3 0

3 years ago