All categories

3 years ago

What are the coordinates of the vertex of the parabola described by the equation below? y = -7(x - 4)2 - 5

2 answers:

7 0

To get the vertex of the parabola we proceed as follows;
y=-7(x-4)^2-5
The above can be written as:
y=-7x^2+56x-117
The values of a,b and c are:
a=-7, b=56 and c=-117
x=-b/(2a)
x=-56/(-7*2)=4
but;
y=-7x^2+56x-117
y=-7(4)^2+56(4)-117
y=-5
Thus;
x=4 and y=-5
The vertex will be at point (4,-5)

lesantik [10]3 years ago

4 0

Answer:

The answer is (4, -5), Hope you have a good day and pass the exam.

Step-by-step explanation:

You might be interested in

For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

5 0

3 years ago

Evaluate the following expression when x = 3 and y = 4: Fraction with x squared plus y cubed in the numerator and 2 plus x in th

Black_prince [1.1K]

The answer is C. 14.6.

By evaluate, they mean substitute in the values of x and y to find the total of the expression, so you get:
(3^2 + 4^3)/(3 + 2) = (9 + 64)/5 = 73/5 = 14.6

I hope this helps!

4 0

3 years ago

Read 2 more answers

If f(x)=ln(sin(2x)), f''(π/4) is equal to

Licemer1 [7]

Use the chain rule to compute the second derivative:

$f(x)=\ln(\sin(2x))$

The first derivative is

$f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}$

$f'(x)=2\cot(2x)$

Then the second derivative is

$f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'$

$f''(x)=-4\csc^2(2x)$

Then plug in π/4 for <em>x</em> :

$f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4$

4 0

3 years ago

A sandwich shop is 70 stores and 70% of the stores are in California the rest of stores are in Nevada how many stars are in Cali

sineoko [7]

49 stores in California
21 stores in Nevada

3 0

3 years ago

Read 2 more answers

Find the surface area of the cube shown below.<br> units 2 1/2

dalvyx [7]

Answer: 37.5

Explanation: find the surface area of one side, which is 2.5*2.5=6.25 then multiply that product by six, since there’s six sides in a square, and you’ll get 37.5

4 0

3 years ago

Read 2 more answers