Question

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.

Answer 1

Answer:

1) The parabola equation faces up

2) The y-intercept = a·b

3) The zeros are x = a and x = b

Step-by-step explanation:

1) The given information are;

f(x) = (x - a)·(x - b) which gives;

f(x) = x² - (b+a)·x + a·b

For an equation of the form a·x² - b·x + c, if a is positive, then the parabola faces up, therefore, the parabola equation, x² - (b+a)·x + ab where a is equivalent to +1 faces up

2) The y-intercept is given at x = 0, which gives;

f(0) = 0² - (b+a)·0 + a·b

The y-intercept = a·b

3) From f(x) = (x - a)·(x - b), when f(x) = 0, we have either;

(x - a) = 0 or (x - b) = 0

Therefore;

The zeros are x = a and x = b