Question 18 (4 points)

Write the equation for a parabola that has x-intercepts (−4.5, 0) and (−2.8, 0) and y-intercept (0, 37.8).

BARSIC [14]

Answer:

$y = 3(x + 4.5)(x + 2.8)$ .

Step-by-step explanation:

Start with the two $x$ -intercepts. The two zeros of the quadratic equation for this parabola are:

$x_1 = -4.5$ , and
$x_2 = 2.8$ .

(These are the $x$ -coordinates of the two $x$ -intercepts.)

By the factor theorem, $x = k$ (where $k$ is a real number) is a zero of a polynomial if and only if $(x - k)$ is a factor of that polynomial.

A quadratic equation is also a polynomial. In this case, the two zeros would correspond to the two factors

$(x - (-4.5)) = (x + 4.5)$ .
$(x - (-2.8)) = (x + 2.8)$

A parabola could only have up to two factors. As a result, the power of these two factor should both be one. Hence, the equation for the parabola would be in the form

$y = a \, (x + 4.5)(x + 2.8)$ ,

where $a$ is the leading coefficient that still needs to be found. Calculate the value of $a$ using the $y$ -intercept of this parabola. (Any other point on this parabola that is not one of the two $x$ -intercepts would work.)

Since the coordinates of the $y$ -intercept are $(0,\, 37.8)$ , $x = 0$ and $y = 37.8$ . The equation $y = a \, (x + 4.5)(x + 2.8)$ becomes:

$37.8 = a \, (0 + 4.5)(0 + 2.8)$ .

Solve for $a$ :

$\displaystyle a = \frac{37.8}{4.5\times 2.8} = 3$ .

Hence the equation for this parabola:

$y = 3(x + 4.5)(x + 2.8)$ .

3 0

3 years ago

Can some one solve this please

Arada [10]

the answer is it would increase

6 0

3 years ago

Read 2 more answers

Solve the system of equations.

sasho [114]

Step-by-step explanation:

y = x² - 3x + 6

y = 2x + 6

y = y

x² - 3x + 6 = 2x + 6

x² - 5x = 0

x(x - 5) = 0

x = 0 and x = 5

y = 2x + 6 and y = 2x + 6

y = 2(0) + 6 and y = 2(5) + 6

y = 0 + 6 and y = 10 + 6

y = 6 and y = 16

(x1,y1) and (x2, y2) = (0,6) and (5,16)

Option → A

8 0

3 years ago

Mary made two 8 ounce drinks each in a separate cup. The first cup has 4 ounces f coffee and four ounces of milk. The second cup

siniylev [52]

Answer:

6 ounces

Step-by-step explanation:

First cup = 4 ounces of coffee + 4 ounces of milk

= 8 ounces drink

Second cup = 6 ounces of coffee + 2 ounces of milk

= 8 ounces drink

She poured 2 ounces from the first cup and 4 ounces from the second cup into the third cup.

Third cup = 2 ounces from the first cup + 4 ounces from the second cup

= 2 + 4

= 6 ounces drink

Ounces of coffee are in the third cup = 6 ounces

8 0

3 years ago

Mrs.Sands teaches 6 different classes per day at the high school. There are 36 students in each class. How many students does sh

lana66690 [7]

Most of the information's that are required for solving this question is already provided in the question. Based on those details the answer to the question can be easily determined.
Number of different classes taught by Mrs. Sands = 6
Number of students in each class = 36
Then
The total number of students taught by Mrs. Sands = (36 * 6)
= 216
So the total number of students that Mrs. Sands teaches is 216. I hope the procedure is clear enough for you to understand. You can always use this procedure for solving similar problems without requiring any help from outside.

3 0

3 years ago

Read 2 more answers