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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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Pls help me
bekas [8.4K]

The composite function combines the palm tree and the seed functions

The composite function is t(d) = 60d + 20

<h3>How to determine the composite functions</h3>

The functions are given as:

Number of palm trees: t(s) = 3s + 20

Number of seeds: s(d) = 20d

The composite function that represents the number of palm trees Carlos can expect to grow over a certain number of days is represented as:

t(s(d))

This is calculated as:

t(s(d)) = 3s(d) + 20

Substitute s(d) = 20d

t(s(d)) = 3 * 20d + 20

Evaluate the product

t(s(d)) = 60d + 20

Rewrite as:

t(d) = 60d + 20

Hence, the composite function is t(d) = 60d + 20

Read more about composite functions at:

brainly.com/question/10687170

4 0
2 years ago
Please help me with this question.. { 8th Grade Math} I don't need an explanation just the answers.
xz_007 [3.2K]

Answer:

45 degrees

2 units

Step-by-step explanation:

A rotation is an Isometry so therefore the 45-45-90 Triangle is the exact same size and shape after the rotation.

3 0
3 years ago
I need some help with this one
Mrac [35]

Answer:

300+90+9

-45=0+40+5

Step-by-step explanation:

399-45=354

8 0
2 years ago
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A center has a center at X(4, -3) and a point on the circle is W(8, 0). What is the location of Y on the diameter WY?
igor_vitrenko [27]

Answer: (0, -6)

Step-by-step explanation:

The center is the midpoint of the diameter, meaning that the coordinates of Y must be (0, -6).

7 0
2 years ago
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary
sashaice [31]

Danielle earned $951.25

Step-by-step explanation:

Multiply her commission by her sales and add her base rate

x=7.25%($4500)+625 or x=0.0725(4500)+625

distribute

x=326.25+625

simplify

x=951.25

8 0
3 years ago
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