How is the graph of the parent function y = x squared transformed to produce the graph of y = 3 (x + 1) squared?

The endpoints of DE and D(-3, y) and x, 6). The midpoint of DE is M(4,2). What is the length of DE.

Natasha_Volkova [10]

If the endpoints of DE where D(-3, y) and E(x, 6) with the midpoint M(4, 2), the length of DE is 16.12 units

The formula for calculating the midpoint is expressed as;

$M(x,y)=(\frac{x_1+x_1}{2}, \frac{y_1+y_2}{2})$

For the x-coordinate points:

X = -3+x/2

4 * 2 = -3 + x

8 = -3 + x

x = 8 + 3

x = 11

Get the value of y;

2 = y+6/2

y+6 = 2 * 2

y + 6 = 4

y = 4 - 6

y = -2

Hence the coordinates of D and E are D(-3, -2) and E(11, 6)

$D=\sqrt{(6-(-2))^2+(11-(-3))^2}\\D=\sqrt{8^2+14^2}\\D=\sqrt{64 + 196}\\D= \sqrt{260}\\D= 16.12units$

Hence the length of DE is 16.12 units

Learn more here; brainly.com/question/22624745

3 0

2 years ago

What is an equation of the line that passes through the point (1, -2) and is parallel

Oliga [24]

Answer:

y = -6x + 4

Step-by-step explanation:

2 parallel lines should have equal slope

Rewrite 6x + y = 92

It is now y = -6x + 92. Slope is -6

So the new equation should also have -6 as the slope.

y = -6x + b

Substitute (1,-2) into this equation

-2 = -6(1) + b

-2 = -6 + b

4 = b

So equation is y = -6x + 4

6 0

3 years ago

Solve the linear equation x + 4 + 3 + 72

elixir [45]

Answer:

x=17

Step-by-step explanation

4x+4=72

-4 -4

4x=68

/4 /4

x= 17

7 0

2 years ago

Read 2 more answers

Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$