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WINSTONCH [101]
3 years ago
13

Identify the turning point of the function f(x)= x^2 -2x + 8 by writing its equation in vertex form . show work

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
7 0
The turning point of a parabola is its vertex.

f(x)=x^2-2x+8\\
f(x)=x^2-2x+1+7\\
f(x)=(x-1)^2+7
The vertex is (1,7)
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PLEASE HELPPP!!!
Tems11 [23]

Answer:

a) -16t^{2}+64t\geq40

b)[2-\frac{\sqrt{6}}{2} , 2+\frac{\sqrt{6}}{2}]

(see attached picture for the number line)

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) h_{max}=64ft

d) t=2s

Step-by-step explanation:

a)

Basically the ball will disappear when it is higher than 40 ft, so we can build the inequality like this:

-16t^{2}+64t\geq40

this is because the function represents it's height, so when the function is greater than or equal to 40, then the ball will disappear.

b) to solve the inequality, first we need to turn the ≥ symbol to an = symbol and solve for t, so we get:

-16t^{2}+64t =40

we can move the 40 to the other side of the equation so we get:

-16t^{2}+64t-40=0

we can factor the equation so it's easier to solve, so we get:

-8(2t^{2}-8t+5) =0

which simplifies to:

2t^{2}-8t+5=0

and we can use the quadratic formula to solve this equation, so we get:

t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}

so we get:

t=\frac{-(-8)\pm\sqrt{(-8)^{2}-4(2)(5)}}{2(2)}

which yields:

2\pm \frac{\sqrt{6}}{2}

and next we need to test the posible intervals to see which one makes the inequality true, the possible intervals are:

(-\infty, 2-\frac{\sqrt{6}}{2}]  for a test value of 0

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}] for a test value of 1

[2+\frac{\sqrt{6}}{2},\infty) for a test value of 4

so next we test each of the values in the original inequality and see if the inequality is true:

(-\infty, 2-\frac{\sqrt{6}}{2}] for a test value of 0

-16(0)^{2}+64(0)\geq40

0\geq40 false

so this is not an answer.

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}] for a test value of 1

-16(1)^{2}+64(1)\geq40

48\geq40

true, so this is an answer.

[2+\frac{\sqrt{6}}{2}, \infty) for a test value of 4

-16(4)^{2}+64(4)\geq40

-16(16)+64(4)\geq40

-256+256\geq40

0\geq40

false, so this is no answer.

So the answer is the interval:

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}]

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) In order to find how high Penelope kick the football, we must find the vertex of the parabola which is gotten when graping the given function (see attached picture)

so we can use the following formula to find the t-value for this maximum height:

t=-\frac{b}{2a}

so we substitute the corresponding values:

t=-\frac{64}{2(-16)}

which yields:

t=2s

next, we can substitute this time into the original function to find the maximum height, so we get:

h=-16(2)^{2}+64(2)

which yields:

h=64 ft

d) We found the answer for d on the previous part where we got that t=2s

6 0
3 years ago
When making pink paint, the art teacher uses the ratio 3:2. For every 3 cups of white paint she uses in the mixture, she needs t
Step2247 [10]
Your answer should be C.

4 0
3 years ago
Daniel worked for 213 hours and earned $18.20.
OleMash [197]

Answer:

2 1/3hrs→ $18.20

1 hr→ $7.80

5 1/4hrs→ $7.80x5 1/4= $40.95

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Factor the expression. -20x + 32
fgiga [73]
Factor -20x+32
which comes out to 4(-5x+8)
answer: 4(-5x+8)
hope this helped :)
8 0
3 years ago
Really need help on this math question! “Jill is draining her pool before winter arrives.
Burka [1]

Answer:

f(x)=2000-8x

Step-by-step explanation:

2000 is initial amount that gets subtracted

8x is the amount of gallons being siphoned out, where x is t, or minutes.

5 0
3 years ago
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