Need help on this please

What is the equation in vertex form of the quadratic function with a vertex at (-1, -4) that goes through (1, 8)?

cestrela7 [59]

Answer:

y = 3(x+1)^2 - 4

Step-by-step explanation:The general form of the equation of a quadratic function whose vertex is (h,k) and whose leading coefficient is a is:

y - k = a(x-h)^2, or

y = a(x-h)^2 - k

Substituting the coefficients of the vertex (-1, -4), we get:

y = a(x + 1)^2 - 4

Substituting the coordinates of the given point, (1,8), we get:

8 = a(1+1)^2 - 4, which simplifies to:

8 = a(2)^2 - 4, or

8 = 4a - 4. Then 4a = 12, and a = 3.

Thus, the desired equation is y = 3(x+1)^2 - 4 (answer j).

5 0

3 years ago

What is the equation of the line that passes through (-5,6) and (3,-10)??

Tanzania [10]

The equation is -2x-4. u can use y2-y1/x2-x1.

7 0

2 years ago

What set of values is apart of the solution set to the inequality 3.5p+14>7p

aalyn [17]

Answer:

q

Step-by-step explanation:

5 0

2 years ago

Given sin(u)= -7/25 and cos(v) = -4/5, what is the exact value of cos(u-v) if both angles are in quadrant 3

solmaris [256]

Given:

$\sin (u)=-\dfrac{7}{25}$

$\cos (v)=-\dfrac{4}{5}$

To find:

The exact value of cos(u-v) if both angles are in quadrant 3.

Solution:

In 3rd quadrant, cos and sin both trigonometric ratios are negative.

We have,

$\sin (u)=-\dfrac{7}{25}$

$\cos (v)=-\dfrac{4}{5}$

Now,

$\cos (u)=-\sqrt{1-\sin^2 (u)}$

$\cos (u)=-\sqrt{1-(-\dfrac{7}{25})^2}$

$\cos (u)=-\sqrt{1-\dfrac{49}{625}}$

$\cos (u)=-\sqrt{\dfrac{625-49}{625}}$

On further simplification, we get

$\cos (u)=-\sqrt{\dfrac{576}{625}}$

$\cos (u)=-\dfrac{24}{25}$

Similarly,

$\sin (v)=-\sqrt{1-\cos^2 (v)}$

$\sin (v)=-\sqrt{1-(-\dfrac{4}{5})^2}$

$\sin (v)=-\sqrt{1-\dfrac{16}{25}}$

$\sin (v)=-\sqrt{\dfrac{25-16}{25}}$

$\sin (v)=-\sqrt{\dfrac{9}{25}}$

$\sin (v)=-\dfrac{3}{5}$

Now,

$\cos (u-v)=\cos u\cos v+\sin u\sin v$

$\cos (u-v)=\left(-\dfrac{24}{25}\right)\left(-\dfrac{4}{5}\right)+\left(-\dfrac{7}{25}\right)\left(-\dfrac{3}{25}\right)$

$\cos (u-v)=\dfrac{96}{625}+\dfrac{21}{625}$

$\cos (u-v)=\dfrac{1 17}{625}$

Therefore, the value of cos (u-v) is 0.1872.

6 0

2 years ago

bridget recieved 1400 from her grandfather as a birthday gift she decided to put the money in an account to save for college the

Simora [160]

Answer:

The amount received after 5 years is 1827.39

Step-by-step explanation:

The amount received by Bridget from his grandfather as the birthday gift = 1400 .

Since he wants to deposit it and save for college, he earns interest rate = 5.4%

He deposited this money for the years = 5 years.

Here, the Present value (PV) is = 1400

Interest rate ( r ) = 5.4% or 0.054

Since the interest rate is compounded semi annually, So, n = 10

Now if we calculate the future value of 1400 with interest rate 5.4 percent:

$\text{The amount received after 5 years} = PV(1 + \frac{r}{2} )^{n} \\$

$= 1400(1 + \frac{0.054}{2})^{10} \\$

$= 1827.39$

Therefore, 1827.39 will be the total money in his account after five years.

5 0

3 years ago