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3 years ago

Consider the quadratic function:

Mathematics

2 answers:

Grace [21]3 years ago

5 0

Answer:

vertex = (4, - 25 )

Step-by-step explanation:

Given a quadratic function in standard form : f(x) = ax² + bx + c : a ≠ 0

The the x- coordinate of the vertex is

$x_{V}$ = - $\frac{b}{2a}$

f(x) = x² - 8x - 9 ← is in standard form

with a = 1, b = - 8, thus

$x_{V}$ = - $\frac{-8}{2}$ = 4

Substitute x = 4 into f(x) for corresponding value of y

f(4) = 4² - 8(4) - 9 = 16 - 32 - 9 = - 25

vertex = (4, - 25 )

Mice21 [21]3 years ago

3 0

Answer:

vertex is (4,-25)

Step-by-step explanation:

$f(x) = x^2 - 8x - 9$

To find out the vertex we use formula

$x=\frac{-b}{2a}$

From the given f(x), the value of a=1, b=-8 and c=-9

Plug in the values in the formula

$x=\frac{-(-8)}{2(1)}$

x=4

Now find the value of y

plug in 4 for x in f(x)

$f(4) = 4^2 - 8(4)- 9=-25$

The value of y is -25

The vertex is (4,-25)

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Question<br><br> Express the inequality x > -1 using interval notation

Nimfa-mama [501]

Step-by-step explanation:

x > -1

x = {0,1,2,...}

$\lang -1,+\infty \rang$

4 0

2 years ago

Heeeeeeeeeelpppppppp meeeeeeee

Step2247 [10]

Answer: The answer is 10.5

Step-by-step explanation: for subtracting the answer is 1.5 and for multplying its 39.375 and last for division its 0.51428571428 *lol*

Have a wonderful day! ^-^

6 0

2 years ago

HELP PLEASE 35 POINTS

postnew [5]

For this case we have:

Let a function of the form $y = f (x)$

By definition, to graph $y = f (x + h)$ , where $h> 0$ , we must move the graph of f (x), h units to the left.

We observe that the red graph has the same form as the black graph, but it is displaced "h" units to the left.

It is observed that $h = 3$

So, if the black graph is given by $y = f (x)$ , the red graph is given by: $y = f (x + 3)$

Answer:

$y = f (x + 3)$

Option A

3 0

2 years ago

Read 2 more answers

Someone pls help me.

nydimaria [60]

I’m here to help.
For this question here you need to use the sine formula for the area of a triangle and figure out the area of the sector

I’ll take you through it step-by-step

Area of the arc:

We only have 68.9 degrees out of 360 and we need to use the formula for the area of a circle.
Formula of a circle = pi x radius squared

68.9/360 x pi x 86.1184= 51.78 (2dp)

Area of triangle:
As you can see we have no height so we must use the sine formula for the area of a triangle.
Formula= 1/2abSinC

You should end up with
0.5 x 9.28x 9.28 x Sin(68.9)= 40.17 (2dp)

Now since you want the area of the segment shaded, just find the difference between these two values.

51.78-40.17 = 11.61
Answer= 11.6cm squared

Hope this helped!

3 0

3 years ago

A bus went halfway from a village to a city at a certain speed. Then it stopped in traffic for an hour. In order to catch up the

k0ka [10]

We have to assume that the speed before being stuck was sufficient to get to the destination on time had there been no delay. Call that speed "s" in km/h.

Since 200 km is "halfway", the total distance must be 400 km.

time = distance / speed
total time = (time for first half) + (delay) + (time for second half)

400/s = 200/s + 1 + 200/(s+10) . . . .times are in hours, distances in km
200/s = 1 + 200/(s+10) . . . . . . . . . . subtract 200/s
200(s+10) = s(s+10) +200s . . . . . . .multiply by s(s+10)
0 = s² +10s - 2000 . . . . . . . . . . . . . .subtract the left side
(s+50)(s-40) = 0
Solutions are s = -50, s = 40

The speed of the bus before the traffic holdup was 40 km/h.

4 0

2 years ago