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3 years ago

5

Factor the polynomials by finding the GCF

1 answer:

Kobotan [32]3 years ago

3 0

3x + 12

The GCF here is 3.

3x / 3 = x
12 / 3 = 4

So we have 3(x + 4)

7y - 7

The GCF here is 7.

7y / 7 = y
-7 / 7 = -1

So we have 7(y - 1)

5x + 30y

The GCF here is 5.

5x / 5 = x
30y / 5 = 6y

So we have 5(x + 6y)

8m + 36n

The GCF here is 4.

8m / 4 = 2m
36n / 4 = 9n

So we have 4(2m + 9n)

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Given the quadratic equation <img src="https://tex.z-dn.net/?f=y%20%3D%202%28x%20-1%29%5E%7B2%7D%20%2B%208" id="TexFormula1" tit

Sunny_sXe [5.5K]

Answer:

Part 1) "a" value is $2$

Part 2) The vertex is the point $(1,8)$

Part 3) The equation of the axis of symmetry is $x=1$

Part 4) The vertex is a minimum

Part 5) The quadratic equation in standard form is $y=2x^{2}-4x+10$

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

if a > 0 then the parabola open upward (vertex is a minimum)

if a < 0 then the parabola open downward (vertex is a maximum)

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

$x=h$

In this problem we have

$y=2(x-1)^{2}+8$ -----> this is the equation in vertex form of a vertical parabola

The value of $a=2$

so

a>0 then the parabola open upward (vertex is a minimum)

The vertex is the point $(1,8)$

so

$(h,k)=(1,8)$

The equation of the axis of symmetry is $x=1$

The equation of a vertical parabola in standard form is equal to

$y=ax^{2}+bx+c$

Convert vertex form in standard form

$y=2(x-1)^{2}+8$

$y=2(x^{2}-2x+1)+8$

$y=2x^{2}-4x+2+8$

$y=2x^{2}-4x+10$

see the attached figure to better understand the problem

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