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sweet-ann [11.9K]
3 years ago
13

Consider the quadratic function:

Mathematics
1 answer:
sdas [7]3 years ago
8 0

Answer:

Step-by-step explanation:

I'm not sure how you are finding this in class, but the easiest way by far is to use the expressions for h and k:

h=\frac{-b}{2a}  and

k=c-\frac{b^2}{4a}

(Just a fun fact:  Those expressions come from the quadratic formula that help us to factor a quadratic equation.)

Filling in for h:

h=\frac{-(-8)}{2(1)}  simplifies to

h = \frac{8}{2}=4

Filling in for k:

k=-9-\frac{(-8)^2}{4(1)}  which simplifies a bit to

k=-9-\frac{64}{4}  which simplifies a bit more to

k=-9-16=-25

The vertex, then, is (4, -25).

You would also find this if you completed the square.  But again, I'm not sure how you're solving for the vertex in class.

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X^3+13x^2+32x+20<br> please help me factorizing above equation
Mazyrski [523]
x^3+13x^2+32x+20=x^3+x^2+12x^2+ 12x+20x+20 =\\\\=x^2(x+1)+12x(x + 1 )+20(x+1 )=(x+1)(x^2+12x+20)=\\\\=(x+1)[(x^2+10x+2x+20)]=(x+1)[x(x +10)+2(x+10))]=\\\\=(x+1) (x +2) (x+10)


7 0
3 years ago
Which graph represents a function
Oduvanchick [21]

Answer:

A

Step-by-step explanation:

Linear as said in it's name is a function that creates (visualy) a straight line.

FROM all the graphs A shows a straight line therefore, the answer.

8 0
3 years ago
Graph the following equations on the graphs below. <br> ( GRAPHING PAPER NEEDED, NOT A WEBSITE )
kodGreya [7K]

First, you want to identify the slopes and y-int.

Equation 1 = y = -2x + 2

Slope = -2

y-int. = 2 or (0,2)

Equationt 2 =  y = 2x + 3

Slope = 2

Y-int.  = 3 or (0,3)

To graph, first plot the y-intercepts. Then do the slopes.

Slope = -2

Down 2 over 1 (to the right)

Slope = 2

Up 2 over 1 (to the right)

Then just connect the dots in a line!

5 0
2 years ago
Find the solution set of this equation.<br> y^2-11y=0 <br> separate the two values with a comma.
Tanya [424]

Answer:

0,11

Step-by-step explanation:

y^2-11y=0

y(y-11)=0 we have transformed the equation into a product

a product can be zero only if one of the factors is 0

so the two solutions are

y=0

and y-11=0  y=11

6 0
3 years ago
Find the distance between the pair of points: (6,−3) and (1,0
rosijanka [135]

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

\sqrt{34}

»»————- ★ ————-««  

Here’s why:

⸻⸻⸻⸻

\text{\underline{The distance formula is:}}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

⸻⸻⸻⸻

\boxed{\text{Calculating the answer....}}\\\\d = \sqrt{(1-6)^2+(0-(-3))^2}\\--------------\\\rightarrow d = \sqrt{(-5)^2+(3)^2}\\\\\rightarrow d = \sqrt{(25+9)}\\\\\rightarrow d =\boxed{ \sqrt{34} }

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.

6 0
3 years ago
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