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4 years ago

Determine the quadratic function f whose graph is given. The vertex is (1,-3) and y-intercept is -2

Mathematics

1 answer:

Nesterboy [21]4 years ago

5 0

Answer:

Vertex form: $f(x)=(x-1)^2-3$

Standard form: $f(x)=x^2-2x-2$

Step-by-step explanation:

A quadratic function in vertex form is $f(x)=a(x-h)^2+k$ where $(h,k)$ is the vertex.

We are given $h=1,k=-3$ .

Let's plug that in:

$f(x)=a(x-1)^2-3$ .

Now let's find $a$ .

We will use the $y$ -intercept $(0,-2)$ to find $a$ .

$f(0)=a(0-1)^2-3$

$-2=a(0-1)^2-3$

$-2=a(-1)^2-3$

$-2=a(1)-3$

$-2=a-3$

$1=a$

So the function in vertex form is:

$f(x)=(x-1)^2-3$ .

In standard form, we will have to multiply and combine any like terms.

Let's do that:

$f(x)=(x-1)(x-1)-3$

$f(x)=x^2-x-x+1-3$

$f(x)=x^2-2x-2$

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3 years ago

I need help simplify 2a^0

Yuliya22 [10]

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3 years ago

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caitlin got a haircut that cost 42.30 she tipped the stylist 8.46. What percent did she tip the stylist?

Julli [10]

Answer:

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Hope This Helps!!!

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3 years ago

A sprinkler sprays water in a circular area up to 30 feet. A radius reduction screw lets people reduce the radius by up to 25%.

tankabanditka [31]

Answer: $1590.63\ ft^2$

Step-by-step explanation:

Given

The sprinkler can water the area up to $30\ ft$ i.e. $30\ ft$ is the radius

If the screw leads to a reduction of 25% in radius, then the new radius is

$r'=(1-0.25)r\\r'=0.75r\\r'=22.5\ ft$

So, the area corresponding to this radius

$\Rightarrow \pi (22.5)^2\\\Rightarrow 1590.63\ ft^2$

Thus, the maximum area that can be covered is $1590.63\ ft^2$

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3 years ago

Do i add up the exponents or subtract? i don't quite understand my homework. if you are going to respond, please send a step by

Naddik [55]

Answer:

2n³ - 3n² - 7n + 3

Step-by-step explanation:

Hi there! Don't worry, polynomials seem hard but you will get them with practice.

I am going to show you 2 methods of multiplying polynomials. These methods are universal, or they work with any polynomial multiplication problem:

<h2>Method 1: Distributive Property</h2>

This is perhaps the most common method. You distribute 1 value to another or multiply each and every single term.

Let's solve it!

(n² - 3n + 1)(2n + 3)
n²(2n + 3) - 3n(2n + 3) + 1(2n + 3)
n²(2n) + n²(3) - 3n(2n) - 3n(3) + 2n + 3 See how I distributed the values?
2n³ + 3n² - 6n² - 9n + 2n + 3

Now, we add up like terms. Like terms should have the same coefficient and should be raised to the same power.

2n³ + 3n² - 6n² - 9n + 2n + 3
2n³ - 3n² - 7n + 3

There you have it! This is how you solve with The distributive Property Method.

<h2>Method 2: Area Model</h2>

This is the next universal method, Area modeling.

Area models can be set up by the number of terms we have. In the first polynomial we have three terms:

Just for this method, keeping the positive signs helps.

For the binomial, we have two terms (hence, binomial)

We set up our are model like this, with the terms laid out as side lengths of a rectangle. (Attachment "A")

Next, we find the area of each individual tile. (Attachment "B")

Now, we add like terms. Something nice about area models is that most of the time, the like terms are matched up in a diagonal. (Attachment "C")

2n³ + 3n² - 6n² - 9n + 2n + 3
2n³ - 3n² - 7n + 3

We end up with the same answer as before.

-Chetan K

7 0

2 years ago