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goblinko [34]
3 years ago
15

1. Describe how factoring a quadratic expression ax2 + bx + c, where a ≠ 1, is different from factoring x2 + bx + c.

Mathematics
2 answers:
Afina-wow [57]3 years ago
4 0
1.  Factoring a quadratic expression ax2 + bx + c, where a ≠ 1, is different from factoring x2 + bx + c because for the former type of expression you have to factor out the value of "a". Then, proceed to the factoring steps as usual.

2. To confirm the equations to be equal with the parent function we do as follows:
<span> (2x – 4)(x + 5) = 2x^2 + 10x - 4x - 20 = 2x^2 + 6x -20
</span><span>(x – 2)(2x + 10) = 2x^2 +10x - 4x -20 = 2x^2 +6x - 20

3. The roots of the quadratic expression represents the values of x that would satisfy the expression. The x-intercepts are the values of x when y is equal to zero, it is where the plot touches intersects the x-axis.</span>
Ulleksa [173]3 years ago
4 0

Answer:

1. Dividing the expressions ax^2+bx+c by a is a different step.

2. Yes, both of these factorization are correct. They are not complete because they can be factored further.

3. The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.

Step-by-step explanation:

1.

To factorize the quadratic expressions ax^2+bx+c first we divide it by a. Then we factorize it same as x^2+bx+c.

It means all the steps of factoring a quadratic expressions ax^2+bx+c and x^2+bx+c are same except the first step, i.e., divide the expressions ax^2+bx+c by a.

2.

The given quadratic expression is

P(x)=2x^2+6x-20

(2x-4)(x+5)=2x(x+5)-4(x+5)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)

(x-2)(2x+10)=x(2x+10)-2(2x+10)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)

The product of factors is equal to the given expression. It means both of these factorization are correct.

They are not complete because they can be factored further.

(2x-4)(x+5)=2(x-2)(x+5)

(x-2)(2x+10)=(x-2)2(x+5)

3.

If the factored form of a quadratic expression is defined as

(x-a)(x-b)

Then the related quadratic equation is

(x-a)(x-b)=0

x=a,b

The roots of the quadratic equation are a and b.

The related function is

f(x)=(x-a)(x-b)

The x-intercepts of the function are a and b because at x=a and x=b the value of function is 0.

The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.

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Which inequality represents all the values of x for y&lt;(or equal to)-6(x-18)-2 when y=46
bearhunter [10]

The value of x is x ≤ 9 for which y ≤ -5(x - 18) - 2 when y = 43.

<h3>What are inequalities and their types?</h3>

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is y ≤ -5(x - 18) - 2.

Now the values of x when y = 43 is,

43 ≤ - 5(x - 18) - 2.

43 ≤ - 5x + 90 - 2.

43 - 88 ≤ - 5x.

- 45 ≤ - 5x.

5x ≤ 45.

x ≤ 9.

learn more about inequalities here :

brainly.com/question/11612965

#SPJ1

8 0
1 year ago
Simplify 3(у- 1) +7 completely.<br> А. Зу+6<br> В. Зу+ 4<br> С. 3y+10<br> D. Зу- 3
marysya [2.9K]

Answer:

B. 3y + 4

Step-by-step explanation:

Step 1:

3 (y - 1) + 7

Step 2:

3y - 3 + 7

Answer:

3y + 4

Hope This Helps :)

4 0
3 years ago
Read 2 more answers
The radius r of a sphere is 8.5mm. calculate the sphere's volume v
IRINA_888 [86]
Volume = 4/3 * PI * r^3
Volume = 4/3 * PI * 8.5^3
<span>Volume = 4.18879</span> * <span> <span> <span> 614.125 </span> </span> </span>
Volume = <span> <span> <span> 2,572.44 cubic centimeters

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4 0
3 years ago
The graph of the quadratic function y = ax^2 + bx + c is given.<br> Find a + b + c.
andrey2020 [161]

Answer:

\frac{145}{24}\approx 6***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

(0,3)

(2,8)

(6,5)

Step-by-step explanation:

I see that the graph crosses at (0,3),(2,8), and (6,5).

The equation y=ax^2+bx+c tells us the y-intercept is c since when x=0 we have y=a(0)^2+b(0)+c=0+0+c=c.

The y-intercept for our graph is 3. Therefore, c=3.

So far we have the equation:

y=ax^2+bx+3.

Let's enter the other points creating a system of linear equations to solve:

8=a(2)^2+b(2)+3

5=a(6)^2+b(6)+3

Let's simplify:

8=4a+2b+3

5=36a+6b+3

Let's subtract 3 on both sides:

5=4a+2b

2=36a+6b

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

-15=-12a-6b

2=36a+6b

Now adding the equations results in:

-13=24a

Divide both sides by 24:

\frac{-13}{24}=a

Now using one of the equations we can find b:

5=4a+2b with a=\frac{-13}{24}

5=4\frac{-13}{24}+2b

5=\frac{-13}{6}+2b

Add 13/6 on both sides:

5+\frac{13}{6}=2b

\frac{30+13}{6}=2b

\frac{43}{6}=2b

Divide both sides by 2:

\frac{43}{2(6)}=b

\frac{43}{12}=b

So we have the equation:

y=\frac{-13}{24}x^2+\frac{43}{12}+3

Let's evaluate a+b+c now:

\frac{-13}{24}+\frac{43}{12}+3

\frac{-13+86+72}{24}

\frac{73+72}{24}

\frac{145}{24}

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