All categories

4 years ago

Write the quadratic function in the form =fx+a?xh2k . then, give the vertex of its graph. =fx+?3x218x28

1 answer:

7 0

Write the quadratic function in the form:
f(x) = a(x-h)² + k

Given Function:
f(x) = 3x² + 18x + 28
Using the completing square method:

 f(x) = 3(x² + 6x + 28/3)

f(x) = 3(x² + 6x + (3)² - (3)² + 28/3)

f(x) = 3[(x+3)² - (3)² + 28/3]

f(x) = 3[(x+3)² - 9 + 28/3]

f(x) = 3[(x+3)² - 27/3 + 28/3]

f(x) = 3[(x+3)² - 1/3]

f(x) = 3(x+3)² - 1

Therefore,
The vertex is (h,k) = (-3,-1)

You might be interested in

Convert 3/18 to a decimal

frutty [35]

3/18 = 0.166667

hope this helps .

3 0

3 years ago

Read 2 more answers

Can someone PLEASE help me!! I'm doing a test and I'm really stuck of this question! Each of the small squares in the figure bel

Arturiano [62]

Answer:

40 meters²

Step-by-step explanation:

Formula for the area of a triangle is $\frac{1}{2} *b*h$

$\frac{1}{2} *10*8=\\5*8=\\40$

The area of the triangle is 40 m²

7 0

3 years ago

Lisa drove 240 miles, then increased her speed by 20 miles per hour for 540 miles. If the second part of the drive took 3 hours

Sever21 [200]

Let u be speed while Lisa drove 240 miles and t be the time in completing 240 miles.

We have been given that Lisa increased her speed 20 mph than initial speed over next 540 miles. So her speed on next 540 miles will be $u+20$ mph.

Further more we are given that she took 3 hours more to complete the next 540 miles of the trip than she took in completing initial 240 miles. So she took $(t+3)$ hours in completing next 540 miles.

Since we know $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Now we will substitute our given values in our equation and find out the unknowns. After substitution we will get two equations and two unknowns.

$u=\frac{240}{t}.........(1)\\
\\
(u+20)=\frac{540}{t+3}........(2)$

Now we will substitute equation 1 in equation 2

$(\frac{240}{t}+20)=\frac{540}{t+3}$

Upon solving this equation, we get

$t=6$

Therefore, total time for Lisa to complete the entire trip is 6+6+3 = 15 hours.

And we know that total distance covered is 240+540 = 780 miles

Hence, average speed

$=\frac{\text{Total Distance}}{\text{Total Time}} = \frac{780}{15} = 52 \text{ miles per hour}$

6 0

3 years ago

Find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1). -5 with multiplicity 3 5 with multiplicity 3 -9

faust18 [17]

Answer:

-5, multiplicity 3; +9, multiplicity 2; -1

Step-by-step explanation:

The roots of f(x) are those values of x that make the factors be zero. For a factor of x-a, the root is x=a, because a-a=0. If the factor appears n times, then the root has multiplicity n.

f(x) = (x+5)^3(x-9)^2(x+1) has roots ...

-5 with multiplicity 3
+9 with multiplicity 2
-1

4 0

3 years ago

Solve the equation using square roots. round your solutions to the nearest hundredth. 5x^2+2=6

JulsSmile [24]

X = 0.89
x = -0.89
two solutions

6 0

3 years ago