1.Write an equation that models the following verbal statement and show/explain how you know your translation is correct.

What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (1, −7) and has (2, 3) as its vertex

kondaur [170]

Answer:

Vertex form: f(x) = -10(x − 2)^2 + 3

Standard form: y = -10x^2 + 40x - 37

Step-by-step explanation:

h and k are the vertex coordinates

Substitute them in the vertex form equation:

f(x) = a(x − 2)^2 + 3

Calculate "a" by replacing "f(x)" with -7 and "x" with 1:

-7 = a(1 − 2)^2 + 3

Simplify:

-7 = a(1 − 2)^2 + 3

-7 = a(-1)^2 + 3

-7 = a + 3

-10 = a

Replace a to get the final vertex form equation:

f(x) = -10(x − 2)^2 + 3

Convert to standard form:

y = -10(x − 2)^2 + 3

Expand using binomial theorem:

y = -10(x^2 − 4x + 4) + 3

Simplify:

y = -10x^2 + 40x - 40 + 3

y = -10x^2 + 40x - 37

6 0

3 years ago

A rectangle has a base of 5 inches and a height of 7 inches. If the dimensions are cut in half, what will happen to the

madreJ [45]

Answer:

It will be one-fourth the original size

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

7+4(r+3)=9r-6 show work pls AND HELP ASAP

ivanzaharov [21]

$\: \: \: \: \: \:$

$= \: \: \: \: r = 5$

Step-by-step explanation:

$7 + 4(r + 3) = 9r - 6$

distribute 4 through the parentheses

$7 + 4r + 12 = 9r - 6$

add numbers

$19 + 4r = 9r - 6$

move the variable to the left hand side and change its sign

$19 + 9r = - 6$

move the constant to the right hand side and change its sign

$4r - 9 = - 6 - 19$

collect like terms

 $- 5r = - 6 - 19$ 

calculate the difference

$- 5r = - 25$

divide both sides of the equation by -5

 $= \: \: \: \: r = 5$ 

<h2>hope it helps</h2>

7 0

3 years ago

F(x) = x ^ 2 . What is g(x) ?

Bond [772]

Given:

The function is:

$f(x)=x^2$

The graphs of functions $f(x)$ and $g(x)$ .

To find:

The function $g(x)$ .

Solution:

We have,

$f(x)=x^2$

The function $f(x)$ is vertically compresses to get the graph of the function $g(x)$ . So, the function $g(x)$ is:

$g(x)=kf(x)$

$g(x)=kx^2$ ...(i)

From the given graph it is clear that the graph of the function $g(x)$ passes through the point (3,3). So, putting $x=3$ and $g(x)=3$ in the above function, we get

$3=k(3)^2$

$3=9k$

$\dfrac{3}{9}=k$

$\dfrac{1}{3}=k$

Putting $k=\dfrac{1}{3}$ in (i), we get

$g(x)=\dfrac{1}{3}x^2$

Therefore, the correct option is D.

6 0

3 years ago

Please i need help.....

Lina20 [59]

Answer:

A.105°

Step-by-step explanation:

Angle at W and V are equal and the angles at T and U are also equal

Hence taking angles at T and U...so as to calculate the value of x

5x + 15 = 3x + 21

5x - 3x = 21 - 15

2x = 6.....hence, x = 3

Then for the angle of VXU;

All angles in a triangle add up to 180°

15(3) + 3(3) + 21 = 75°...then subtract from 180°..so as to obtain angle at VXU

180 - 75 = 105°

7 0

3 years ago