1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leni [432]
3 years ago
11

Find the vertex of the graph of f(x) = x2 + 4x - 5.

Mathematics
1 answer:
Fofino [41]3 years ago
7 0
You can solve this in two ways.

1. Graphical. Plot the graph for x between -5 and 1 (see attachement).
The vertex of the graph is the peak of the curve, which has the coordinates x=-2, y=-9.

2. Analytical. Calculate the derivative of the function f(x)
\frac{df}{dx}=2x+4
Solve the equation:
2x+4=0
will give the solution x=-2.
Replace x=-2 in the f(x) function and you'll get the value of y:
(-2)^2+4 \cdot (-2)-5=4-8-5=-9

You get the same answer: x=-2, y=-9

So the answer is
<span>B. (-2, -9)</span>

You might be interested in
The table represents the function f (x) = 2 x + 1.
Salsk061 [2.6K]

Answer:

C

Step-by-step explanation:

In the table, we are given the points [ (-3, -5), (2, y), (5, 11), (8, 17) ]

We are given the equation [ f(x) = 2x + 1 ] where 2 = slope and 1 = y intercept.

We need to find the value of "y".

y2-y1/x2-x1

y-(-5)/2-(-3) = 2

y+5/5 = 2

y = 5

Best of Luck!

5 0
3 years ago
Read 2 more answers
What is the equation of the line?
spin [16.1K]

Answer:

y=1/2x+2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(0,2) and (-4,0).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m= 0 - 2-4 - 0 or... m= -2-4 or... m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (-4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=1/2 × 0+b, or solving for b: b=2-(1/2)(0). b=2.

(-4,0). y=mx+b or 0=1/2 × -4+b, or solving for b: b=0-(1/2)(-4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (-4,0)

is

y=1/2x+2

4 0
3 years ago
Which equation matches the hanger diagram? <br> pls help !!!
telo118 [61]
The answer is D

Because there are two x’s

And 5 number 1’s

So 2x=5
6 0
2 years ago
Read 2 more answers
Simplify: 7ax3+5x2a-9a÷3<br>​
posledela
1)Calculate the product:
21a + 10a - 3a
2)Collect like terms:
28a
Answer:
28a

8 0
3 years ago
Holly has 65 stamps in het collection. To expand the collection, she is planning to buy some books of stamps
ahrayia [7]

Answer:

i think if she buys 5 books the she will have 90 stamps cuz 1 book cost 18 stamps then 5 books = <u>18x5=90</u>

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • WILL GIVE THE BRAINLIEST! Which of the following inequalities can be represented by the graph?
    5·1 answer
  • Find the difference: 7 7/8-3 1/4
    12·1 answer
  • A student club has 9 members. How many ways can the club choose a president, vice president, and treasurer?
    12·1 answer
  • Solve the equation <br> (If possible please show work)
    9·2 answers
  • Suppose that the x-intercepts of the graph of y=f(x) are -9 and 3. What are the x intercepts of y= f(x+3)
    14·1 answer
  • Help <br> me <br> With this math problem
    5·1 answer
  • QUESTION 4: BUSINESS DECISIONS [20 MARKS]
    13·1 answer
  • A train left a station at 8:13 a.m. arriving at its destination at 4:52 p.m. If the stations are 527.65 miles apart, calculate t
    12·1 answer
  • What’s the volume of the cylinder i need help<br> please !!!
    7·1 answer
  • Help meeeeeeeeeeeeeee
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!