Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.

1. The parabola opens up (in the shape of a "u")

2. The y intercept is a·b

3. The zeros occur at points x = a or b

Step-by-step explanation:

f(x) = y = (x - a)(x - b) = x²-a·x-b·x+a·b

y - a·b = x²-a·x-b·x = x² -x·(a + b)

y - a·b + (a + b)²/4 = x² -x·(a + b) + (a + b)²/4 = (x - (a + b)/2)²

y = (x - (a + b)/2)² + a·b - (a + b)²/4

Hence since the general form of the equation of the parabola is y = a(x - h)² + k

1. Comparing, we have a = +1 which indicates that the parabola opens up

The y intercept is found by placing x = 0 as follows;

y = (0 - (a + b)/2)² + a·b - (a + b)²/4 = a·b

The zeros is the x intercept, where y = 0 which is found as follows;

y = (0 - (a + b)/2)² + a·b - (a + b)²/4 = a·b

0 = (x - (a + b)/2)² + a·b - (a + b)²/4

Hence from the initial equation, f(x) = y = (x - a)(x - b) when y = 0, x = a or b

Hence the zeros occur at points x = a or b.

step-by-step explanation:

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.