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3 years ago

What is the vertex and axis of symmetry for y=4x^2-12x+9?

Mathematics

1 answer:

VLD [36.1K]3 years ago

4 0

Answer:

axis of symmetry x=3/2

vertex (3/2, 0)

Step-by-step explanation:

to find the axis of symmetry we use h = -b/2a

where ax^2 + bx+c

h = -(-12)/2(4)

h= 12/8

h = 3/2

the axis of symmetry is x = 3/2

the x coordinate of the vertex is h x=3/2

to find k, the y coordinate of the vertex, substitute x=3/2 into the equation

y=4x^2-12x+9

y=4(3/2) ^2-12(3/2)+9

= 4 (9/4) - 6*3 +9

= 9-18+9

= 0

the vertex (3/2, 0)

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Solve −3x=2x2−4<br> using the Quadratic Formula.

otez555 [7]

Answer:

-3x= 2×2-4

Step-by-step explanation:

-3x= 4-4

-3x= 0

divide both sides by the co-efficient of x

-3x/-3= 0÷-3

x= 0/-3

x = 0

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3 years ago

Alex invests $2,000 in a company's stock. After a year, the value of Alex's stock has increased to $2,500. What rate of return h

Kay [80]

The rate of interest is 25%

<u>Explanation:</u>

Given:

Principal, P = $2,000

Amount, A = $2500

Time, t = 1 year

Rate of Interest, r = ?

We know:

$Amount = P(1+\frac{r}{100})^t$

On substituting the value we get:

$2500 = 2000 (1 + \frac{r}{100})^1\\ \\\frac{25}{20}= (1+\frac{r}{100})\\$

$\frac{5}{20} = \frac{r}{100}\\ \\r = \frac{100 X 5}{20} \\\\r = 25$

Therefore, the rate of interest is 25%

5 0

3 years ago

Read 2 more answers

An artist plans to sell $300 of prints online each week. This month, she is within $22 of her goal.

monitta

The minimum and maximum amounts that the artist received for her products are 278 and 322

<h3>Part A: Define a variable and write an absolute value equation to represent the scenario.</h3>

Let the number of prints remaining be x.

The given parameters are:

Total = 300

Amount = 22 within her goal

So, we have the following absolute value equation

|x - 300| = 22

<h3>Part B: Solve the equation, showing all steps.</h3>

In (a), we have:

|x - 300| = 22

Remove the absolute bracket

x - 300 = 22 and x - 300 = -22

Add 300 to both sides

x = 322 and x = 278

<h3>Part C: What are the minimum and maximum amounts that the artist received for her products?</h3>

The minimum and maximum amounts that the artist received for her products are 278 and 322

Read more about absolute value equation at

brainly.com/question/17795998

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2 years ago

Solve for − ∣ x − 2 ∣ + 4 ≤ 0

MakcuM [25]

Answer:

x ≥ 6 or x ≤ -2

Step-by-step explanation:

- I x - 2 I + 4 ≤ 0

- I x - 2 I ≤ -4

I x - 2 I ≥ 4

x - 2 ≥ 4 or x - 2 ≤ -4

x ≥ 6 or x ≤ -2

5 0

3 years ago

2. Find the common difference and the recursive formula. a. 22, 19, 16, 13, …

Musya8 [376]

Answer:

The common difference d is d = -3

The recursive formula is: $\mathbf{a_n=a_{n-1}-3}$

Step-by-step explanation:

We need to find the common difference and the recursive formula.

a. 22, 19, 16, 13, …

First we will find common difference

The formula of arithmetic sequence is: $a_n=a_1+(n-1)d$

where a_n is nth term, a_1 is 1st term and d is the difference

Looking at the sequence we get: a_1=22, a_2=19

Using these values we can find d, the common difference

$a_n=a_1+(n-1)d\\put\:n=2, a_2=19, a_1=22\\19=22+(2-1)d\\19=22+d\\d=19-22\\d=-3$

So, the common difference d is d = -3

Now, we will find the recursive formula:

The recursive formula is of type: $a_n=a_{n-1}+d$

We have found common difference d = -3

So, the recursive formula will be:

$a_n=a_{n-1}+d\\a_n=a_{n-1}+(-3)\\a_n=a_{n-1}-3$

The recursive formula is: $\mathbf{a_n=a_{n-1}-3}$

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3 years ago