Mathematics, 19.08.2019 17:30 emilie3849

What is a. 11/12 - 7/12 b. 1/2 + 1/8 + 3/4 c. 3/4 - 1/6 ( all in simplified mode )

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A. when subtracting fractions with the same denominator, simply subtract the numerators and keep that number over the original denominator. Thus 11/12-7/12 becomes 4/12. But, this answer is not reduced because 4 is a factor of both the numerator and the denominator. Thus, divide 4 by 4 and 12 by 4 to get the new numerator and denominator. Your final fraction is 1/3.

b. In this expression, the fractions do not all have the same denominator, so you cannot subtract them yet. Your largest denominator is 8 but not all the other denominators are factors of 8. So to make a common denominator with all the fractions, you need to find a number that all the denominators are factors of. One example in this case is 24. Each of these fractions must then be expressed in terms of this common denominator. To do this, you need to find what can be multiplied by the original denominator to make 24. In other words, divide 24 by the original denominator and multiply that answer by the original numerator. In the case of 1/2, 24/2 is 12 and 12 x 1 is 12. Thus, the new fraction is 12/24. The second fraction is also done this way: 24/8=3 and 3x1 is 3 so the new fraction is 324. The third fraction should be handled the same way: 24/4 is 6 and 6x3 is 18 so the new fraction is 18/24. Finally, in 1/6, 24/6 is 4 and 4x1 is 4 so the new fraction is 4/24. Then, like the previous problem, when you perform 12/24 + 3/24 + 18/24-4/24= 29/24. Since 29 is larger than 24, this should be reduced. Do this by subtracting the denominator from the numerator and keep the remaining fraction. The final answer is 1 and 5/24.

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Answer from: Quest

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

as, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

hope this : )

Use the parabola tool to graph the quadratic function f(x) = -2(x+4)2 - 3 graph the parabola by firs

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