Respuesta :
Given:
Create a unique parabola in the pattern f(x) =( x-a)(x-b).
Required:
Describe the direction of the parabola and determine the y-intercept and zeros.
Explanation:
Lets first learn some concepts:
Direction of the parabola can be determined by the value of a. If a is positive, then the parabola faces up (making a u shaped). If a is negative, then the parabola faces down (upside down u).
Y-intercept:
To find the y-intercept, set x = 0 and solve for y.
Zeros:
The zeros of a function are the values of x when f(x) is equal to 0.
We have function
[tex]f(x)=(x-a)(x-b)[/tex][tex]\begin{gathered} \text{ Direction of parabola}: \\ f(x)=x^2-(a+b)x+ab \\ \text{ Here, Leading coefficient is 1. So, direction of parabola will be upward.} \end{gathered}[/tex][tex]\begin{gathered} Y-intercept: \\ \text{ Put }x=0\text{ and we will get }y=ab \end{gathered}[/tex][tex]\begin{gathered} Zeros: \\ (x-a)(x-b)=0 \\ x=a,x=b \end{gathered}[/tex]Answer:
The direction of parabola is upward, y intercept equals ab and zeros are x = a, b.
