The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph?

Answers

Answer 1

Answer:

The coordinates of the vertex of the graph are (-2, -9).

Further explanation

The quadratic function is described by the standard equation $\boxed{ \ f(x) = ax^2 + bx + c \ }.$ The graph of a quadratic function is called a parabola.

We have the quadratic function $\boxed{ \ f(x) = x^2 + 4x - 5 \ }.$

We identify the coefficients a, b, and c. For this equation, $\boxed{ \ a = 1, b = 4, and \ c = -5 \ }$
The axis of symmetry is $\boxed{ \ x = h = -(b)/(2a) \ }$ , i.e., $\boxed{ \ x = h = -(4)/(2(1)) \rightarrow h = -2 \ }.$ Thus, the statement in the question for the symmetry axis x = -2 is correct.
The vertex (or turning point) is $\boxed{ \ (h, k) \ },$ where $\boxed{ \ k = f(h) \ }$ or $\boxed{ \ k = (b^2 - 4ac)/(-4a) \ }$
The parabola opens upward because a > 0, resulting in a vertex that is a minimum.

Finding the minimum value is as follows:

$\boxed{ \ k = f (-2) = (-2)^2 + 4(-2) - 5 \rightarrow k = -9 \ }, or$
$\boxed{ \ k = (4^2 - 4(1)(-5))/(-4(1)) = -(36)/(4) \rightarrow k = -9 \ }$

Therefore, the coordinates of the vertex of the graph are (h, k), i.e., $\boxed{\boxed{ \ (-2, -9) \ }}$

Other components:

The y-intercept of the quadratic function f(x) = x² + 4x - 5 is (0, c), i.e., the point $\boxed{ \ (0, -5) \ }.$
The factorization of f (x) = x² + 4x - 5 becomes f(x) = (x + 5)(x - 1). Then we get the x-intercepts at $\boxed{ \ (-5, 0) \ and \ (1, 0) \ }$

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Keywords: the axis of symmetry, for a function, f(x) = x² + 4x − 5, x = −2, which is the graph of f(x) = (x - 1)(x + 4), what, the coordinates of the vertex of the graph, the x-intercept, quadratic function, a standard equation, the y-intercept, parabola, upward, the minimum value

Answer 2

Answer:

Based on the calculations, the coordinates of the vertex(h, k) of this graph are equal to (-2, -9).

The standard form of a quadratic equation.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Note: The graph of any quadratic function is known as a parabola.

From the given quadratic function, we have:

f(x) = x² + 4x - 5

For its coefficients, we have:

a = 1.

b = 4.

c = -5.

Next, we would determine the coordinates of the vertex of this graph:

x = h = -b/2a

h = -4/2(1)

h = -4/2

h = -2.

Also, we can deduce that the parabola of this graph opens upward because "a" is greater than zero (0), which produces a vertex that is a minimum:

f(h) = k

f(-2) = k = (-2)² + 4(-2) - 5

f(-2) = k = 4 - 8 - 5

k = -9.

Vertex (h, k) = (-2, -9).

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What is the mean of the data set?12, 17, 16, 10, 20, 13, 14, 14, 12, 12, 19, 18

A.14.00

B.14.75

C.13.50

D.15.75

Answers

The answer is given by the second choice: letter B. 14.75 is the answer because to get the mean, you should add all the numbers and then divide it by how many numbers there are. For example, in this case, you add 12, 17, 16, 10, 20, 13, 14, 14, 12, 12, 19, 18 to each other. You will get the answer 172. After that, you should divide 172 by 12 because there are 12 numbers in the data set.

the answer is B because if you add all the numbers up and divide then by the amount of numbers there are then you will end up with the mean

A five minute drive would be how long of a walk?

Answers

Time to complete the distance ( walk time ) ≈ 10 minutes

Hi your question is incomplete but I will provide the general principles on how to resolve this kind of problems

The variables to be considered are :

Velocity/speed
distance/displacement
Time

To determine how long a five minute drive would take a walk to complete

first step : determine the distance

speed = distance / time

assume distance = x

speed = x/5

second step : assume speed of car

lets assume the speed of the car = 20 m/minutes

20 = x / 5

therefore x ( distance ) = 20 * 5 = 100 meters

assume walking speed = 10 m/minutes

y ( time to complete distance ) = distance / speed = 100 / 10 = 10 minutes

Hence based on my assumptions walk time = 10 minutes

learn more : brainly.com/question/23936119

Answer:

11 minutes walking

Step-by-step explanation:

What are the zero(s) of the function f(x) = the quantity of 5 x squared minus 25 x, all over x? x = 5 x = 0 and x = 5

Answers

Answer:

x=5

Step-by-step explanation:

$f(x)= (5x^2-25x)/(x)$

To find out zeros we replace f(x) with 0

$0= (5x^2-25x)/(x)$

Now solve for x

first we divide the numerator by x

$0=5x-25$

Now we facor out GCF 5

$0=5(x-5)$

Divide by 5 on both sides

$0=x-5$

Add 5 on both sides

x= 5

zero of the function is x=5

(5x^2-25x)/x
simplify
((x)(5)(x-5))/x=5(x-5)=5x-25=f(x)
(just fyi, that x we cancled is a hole)
set to zero
5x-25=0
5x=25
divide 5
x=5

zeroe is at x=5
or (5,0)

x=5 is answer

6 squared divided by 2(3) plus 4 =

Answers

6 squared divided by 2(3) plus 4 is equal to 10.

To evaluate the expression 6 squared divided by 2(3) plus 4, follow the order of operations (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right):

Here, from the given expression, we get,

6 squared means 6 raised to the power of 2,

which is $6^2 = 6 * 6 = 36.$

Perform the multiplication inside the parentheses.

2(3) means 2 times 3,

which is 2 * 3 = 6.

Now, the expression becomes:

36 ÷ 6 + 4 [Perform the division]

=>36 ÷ 6 = 6 [Perform the addition]

=> 6 + 4 = 10

The final result is 10.

So, 6 squared divided by 2(3) plus 4 is equal to 10.

To learn more on Expression click:

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6²/2(3) +4

6²=36
2(3)=6
So now we have
36/6 + 4 which is 6 + 4 which is 10.

Select the symbol = (equal to) or ≠ (not equal to) to make the expression true.{1, 2, 3, 4, 5} ? {whole numbers between 1 and 5 inclusive}

Answers

I'm not sure whether '1 and 5 inclusive' means that both 1 and 5 are included or only 5.
If it's the former, then $\{1,2,3,4,5\}=\text{whole numbers between 1 and 5 inclusive}$

Answer:

the correct answer is not equal to or the crossed out equal sign

Step-by-step explanation:

Odyssey

Consider the division expression LaTeX: 7\frac{1}{2}\div27 1 2 ÷ 2. Select all multiplication equations that correspond to this division expression.

Answers

Answer:

2 x ? = 7 1/2 and ? x 2 = 7 1/2

Step-by-step explanation:

This is the answer because it didn't show the answer so all you have to figure out is the multiplication problem that goes with the division problem. So 2 x ? = 7 1/2 and ? x 2 = 7 1/2 you don't have to include the answer all you have to include is where the answer will do if you DID have the answer. These two are correct because the multiplication number can go in any order.

I know this might not be the best step-by-step explanation ever but I truly tried but the answer is correct.

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