MATHEMATICS HIGH SCHOOL

The function f(t) = 4t2 − 8t + 6 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground

Answers

Answer 1

Answer:

Answer:

The correct option is 3.

Step-by-step explanation:

The vertex form of a parabola is

$f(x)=a(x-h)^2+k$ .... (1)

where a, h, and k are integers, and interpret the vertex of f(t). (h,k) is the vertex of the parabola.

The given function is

$f(x)=4t^2-8t+6$

It can be written as

$f(x)=4(t^2-2t)+6$

If an expression is defined as $x^2+bx$ , then we need to add $((b)/(2))^2$ to make it perfect square.

In the expression $t^2-2t$ the value of b is -2. So, we nned to add and subtract $((-2)/(2))^2$ in the parenthesis.

$f(x)=4(t^2-2t+1^2-1^2)+6$

$f(x)=4(t^2-2t+1)+4(-1)+6$

$f(x)=4(t-1)^2-4+6$

$f(x)=4(t-1)^2+2$ .... (2)

The vertex form of the parabola is $f(x)=4(t-1)^2+2$ .

From (1) and (2), we get h=1 and k=2. It means the vertex of the parabola is (1,2). Vertex of upward parabola is point of minima. So the minimum height of the roller coaster is 2 meters from the ground.

Therefore the correct option is 3.

Related Questions

Please help me with this equation
Cristine's middle school has a total of 900 students and 45 teachers. The local high school has 110 teachers and a student-teacher ratio proportional to the middle school's. How many students will Cristine find when she gets to high school? A) 900 B) 1100 C) 2200 D) 2500
What is the answer to this problem and how do u solve it. -8 - 9 =
*****Write a polynomial using the roots -3,5i. PLEASE HELP IM SO LOST!!!
Albert used 3/8 of a half gallon of paint. What fraction of a gallon of paint did he use?

What is the quotient (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

Answers

Answer:

Quotient: $2x^2+x-3$

Please see the attachment.

Step-by-step explanation:

Given: $(2x^4-3x^3-3x^2+7x-3)/ (x^2-2x+1)$

We are given rational expression and need to find quotient.

Using long division method to find the quotient.

First we get rid of $2x^4$ by $x^2$

$x^2-2x+1$ ) $2x^4-3x^3-3x^2+7x-3$ ( $2x^2+x-3$

$-2x^4+4x^3-2x^2$

$x^3-5x^2+7x$

$-x^3+2x^2-x$

$-3x^2+6x-3$

$3x^2-6x+3$

$0$

Hence, The quotient of division is $2x^2+x-3$

Here you have two polynomials:

1. The dividend - $f(x)=2x^4 - 3x^3 - 3x^2 + 7x - 3$

2. The divisor - $g(x)=x^2 - 2x + 1$ .

Since divisor is perfect square $g(x)=x^2 - 2x + 1=(x-1)^2$ , you should check what is the quotient after division f(x) by (x-1):

$f(x)=2x^4 - 3x^3 - 3x^2 + 7x - 3=(x-1)(2x^3-x^2-4x+3)=(x-1)(x-1)(2x^2+x-3)=(x-1)^2(2x^2+x-3)=g(x)(2x^2+x-3).$

Then the quotient is $2x^2+x-3$ .

Each Friday, the school prints 400 copies of the school newsletter. The equation c = 400w models the relationship between the number of weeks and the total number of copies of the newsletters printed. What is true of the graph of this scenario

Answers

A viable point on the graph is ( 8, 3200 )

The values of w must be... Any WHOLE number.

C=400w can be written as y=400x. This is the equation of a line with slope 400 and y-intercept of 0.
The slope of positive 400 represents the number of copies printed each week. Since the slope is positive, the number of copies increases each week.

Find the value of the following:|-15|.

Answers

Answer:

The answer is 15 because that absolute value for anything is 15. No matter what number

Step-by-step explanation:

In the system -12c+3d=6 and -3c+6d=-9, which expression could you use for substitution?. A. d=-1/2c-3/2. B.c=-2d+3. C.c=1/4d-1/2. D. d=4c-2

Answers

The system:
- 12 c + 3 d = 6
- 3 c + 6 d = - 9
----------------------
The 1st equation:
- 12 c = - 3 d + 6 / * ( - 1) ( multiple both sides by -1 )
12 c = 3 d - 6 / : 12 ( divide both sides by 12 )
c = d / 4 - 1/2
Answer:
C ) c = 1/4 d - 1/2

Simplify.
10 – 5.3 • (–4 + –6)
a. 63
b. 47
c. –43
d. –47