Can someone me with this worksheet

1. To find for the linear function from this problem, we use the formula:

x/a + y/b = 1

where a is the x intercept and b is the y intercept

x/-9  +  y/3 = 1

Multiply everything by -9:

x – 3y = -9

Rearranging:

3y = x + 9

y = (1/3) x + 3

2. The general form of a linear function is:

y = mx + b

where m is the slope and b is the y-intercept

y = (-2/5) x + b

when y = 0, x = 1 therefore the b is:

0 = -2/5 + b

b = 2/5

y = (-2/5) x + 2/5

3. We create two equations from the general form y = mx + b or f(x) = mx + b

-5 = (1/6) m + b

-10 = (1/2) m + b

Subtract the two equations:

-5 - -10 = (1/6 – ½) m

5 = -1/3 m

m = -15

y = -15x + b

using any pair to get the value of b:

-5 = -15 (1/6) + b

b = -2.5

y = -15x – 2.5

4. same steps with number 3

-2/3 = (1) m + b

2 = (2/3) m + b

Subtract the two equations:

-2/3 - 2 = (1 – 2/3) m

-8/3 = 1/3 m

m = -8

y = -8x + b

using any pair to get the value of b:

2 = -8(2/3) + b

b = 22/3

y = -8x + 22/3

5. From the graph we have the points:

(-5, 4) and (4, -4)

So we create two equations:

4 = (-5) m + b

-4 = (4) m + b

Subtract the two equations:

4 - -4 = (-5 - 4) m

8 = -9 m

m = -8/9

y = (-8/9) x + b

using any pair to get the value of b:

4 = (-8/9) (-5) + b

b = -4/9

y = (-8/9) x – 4/9

6. From the graph we have the points:

(2, -5) and (4, 6)

So we create two equations:

-5 = (2) m + b

6 = (4) m + b

Subtract the two equations:

-5 - 6 = (2 - 4) m

-11 = -2 m

m = 5.5

y = 5.5 x + b

using any pair to get the value of b:

-5 = 5.5 (2) + b

b = -16

y = 5.5 x – 16

7. We can actually solve this easily by plotting the points. We can see that by plotting the points, a curve line is created, not a straight one.

<check the graph photo attached>

8. Let us say that the x intercept, a = 1 and the y intercept, b = 1. Prove that slope m = -1

From the equation:

x/a + y/b = 1

x/1 + y/1 = 1

x + y = 1

y = -x + 1

Hence slope is m = -1

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 : )

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2