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3 years ago

Use the parabola tool to graph the quadratic function.

Mathematics

1 answer:

prisoha [69]3 years ago

4 0

Answer:

Step-by-step explanation:

Simply by comparing the given

f(x)=(x-2)^2-3 to

f(x) = (x-h)^2 + k, we see that h = 2 and k = -3, which tells us that the vertex of the graph is (2, -3). This parabola opens up because the coefficient of (x-2)^2 is +1.

Evaluating f(x)=(x-2)^2-3 at x = 4 (an arbitrary value), we see that

f(4) = (4-2)^2 - 3 = 4 - 3 = 1.

The point (4, 1) is also on the graph of this parabola.

Graph the vertex (2, -3) and the arbitrarily chosen point (4, 1). Remember that (2, -3) is the minimum of this function, so for x other than 2, the y-value is greater than -3.

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How many Dimes and Quarters

8_murik_8 [283]

Answer:

Julian has 16 dimes and 6 quarters

Step-by-step explanation:

Let's suppose Julian has q quarters and d dimes

The total coins are 22, that is

q+d=22

q=22-d [1]

The total amount of money he has is 310 cents which are made of 10d dimes and 25q quarters

10d+25q=310

Simplifying by 5

2d+5q=62

Using the relation [1]

2d+5(22-d)=62

2d+110-5d=62

3d=48 => d=16

q=22-16 = 6

So Julian has 16 dimes and 6 quarters

5 0

3 years ago

Vanya collects vintage albums. Each storage unit holds 16 albums. She gave 3 albums to her cousin as a graduation present. Which

damaskus [11]

Answer:

Step-by-step explanation:

vintage gave her cousin 3 albums when she had 16

so y=16x-3.

7 0

3 years ago

Twenty gremlins and fifteen imps are at the Annual Mischief Convention. The imps have had a lot of in-fighting lately and refuse

harina [27]

Answer:

490

Step-by-step explanation:

Let us first count the handshakes between two gremlins. There are 20 gremlins, so there must be 20*19/2=190 handshakes between two gremlins, making sure to divide by two to avoid over-counting.

There are 15 imps that shake hands with each of the 20 gremlins, which makes 15* 20 = 300 handshakes between imps and gremlins.

Adding these up, you have $300 + 190 = 490 total handshakes.

Hope this helps!

3 0

3 years ago

Read 2 more answers

What is the area, in square inches, of the isosceles trapezoid below?

Nostrana [21]

Area of a trapezoid: (top + bottom)/2 x height

Area = (6.5 + 15.1)/2 x 5

Area = 21.6/2 x 5

Area = 10.8 x 5

Area = 54 square inches.

3 0

3 years ago

A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

never [62]

The correct answer is:

46.6 days

Explanation:

The general form for exponential growth is

$A=p(1+r)^t$ , where A is the total amount, p is the initial amount, r is the percent of growth, and t is the amount of time (in this case, days).

We do not know the initial amount, the total amount, or the amount of time. We do know that r, the percent of growth, is 1.5%; 1.5% = 1.5/100 = 0.015:

$A=p(1+0.015)^t$

We also know we want the total amount, A, to be twice that of the initial amount, p:

$2p = p(1+0.015)^t
\\
2p=p(1.015)^t$

Divide both sides by p:

$\frac{2p}{p}=\frac{p(1.015)^t}{p}
\\
\\ 2=1.015^t$

Using logarithms to solve this,

$\log_{1.015}(2)=t
\\
\\46.6=t$

8 0

4 years ago

Read 2 more answers