All categories

3 years ago

Fit a quadratic function to these three points: (-2,8), (0, -4), and (4, 68) Respuesta

Mathematics

1 answer:

zloy xaker [14]3 years ago

3 0

Answer:

f(x) = 4x^2 + 2x - 4.

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8) ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8 For (0, -4) we have:

0 + 0 + c = -4 so c = -4. For (4, 68) we have:

16a + 4b + c = 68

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72 Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

You might be interested in

Marr you made 3 gallons of punch for a party when the party was over he had 3 quarts of punch left over how many quarts of punch

Inga [223]

The guest drank 9 quarts at the party

5 0

3 years ago

If I was making cupcakes and brownies for my school fundraiser and the brownies needed 1.28cups of sugar and the cupcakes needed

xxMikexx [17]

You need A lot of sugar

5 0

3 years ago

Read 2 more answers

Use the difference of squares pattern to factor the polynomial.x2 − 16y2 how would I do this

love history [14]

The general rule for difference of two squares is that when factorised it can be written in the form (a+b)(a-b) where a is the square root of the first part of the function and b is the square root of the second part of the function.
From this we can find the square root of x² to find a and the square root of 16y² to find b.
In this case √x²=x and √16y²=4y
Therefore fully factorised it can be written as (x+4y)(x-4y)

6 0

3 years ago

Which is a correct definition of perpendicular lines?

djyliett [7]

It would be B: a set of points that extends infinitely in two directions

4 0

2 years ago

4C. Quintin is using the three different shaped

Sauron [17]

The smallest number of tiles Quintin will need in order to tile his floor is 20

The given parameters;

number of different shapes of tiles available = 3

number of each shape = 5

area of each square shape tiles, A = 2000 cm²

length of the floor, L = 10 m = 1000 cm

width of the floor, W = 6 m = 600 cm

To find:

the smallest number of tiles Quintin will need in order to tile his floor

Among the three different shapes available, total area of one is calculated as;

$A_{one \ square \ type} = 5 \times 2000 \ cm^2 = 10,000 \ cm^2$

Area of the floor is calculated as;

$A_{floor} = 1000 \ cm \times 600 \ cm = 600,000 \ cm^2$

The maximum number tiles needed (this will be possible if only one shape type is used)

$maximum \ number= \frac{Area \ of \ floor}{total \ area \ of \ one \ shape \ type} \\\\maximum \ number= \frac{600,000 \ cm^2}{10,000 \ cm^2} \\\\maximum \ number= 60$

When all the three different shape types are used we can get the smallest number of tiles needed.

The minimum or smallest number of tiles needed (this will be possible if all the 3 different shapes are used)

$3 \times \ smallest \ number = 60\\\\smallest \ number = \frac{60}{3} \\\\smallest \ number = 20$

Thus, the smallest number of tiles Quintin will need in order to tile his floor is 20

Learn more here: brainly.com/question/13877427

3 0

2 years ago