Question

Create a unique parabola in the pattern f(x)=(x-a)(x-b). Pick integers other than one or zero for a and b. let a= 1 and b= 2 f(x)= (x-1)(x-2) = x²-2x-x+2 = x²-3x+2 (this is the one I have made and just need help with the other parts) Describe the direction of the parabola. (Hint: How can you tell if a parabola will open upwards or downwards) Determine the y-intercept. (Hint: Using your equation, set the x’s equal to zero and solve for y) Determine the zeros. (Hint: Using your equation, set y = zero, factor, and solve for x.

Answer 1

Answer:

a) parabola opens upwards  

b) y-intercept    y = 2

c) x₁ = 1         x₂  =  2

Step-by-step explanation:

y = x² - 3x + 2

This  parabola is open upwards since the coefficient of x² is positive (1)

b) y-intercept is when  x = 0 then

y = (0)² - 3*(0) + 2

y-intercept    y = 2

to determine zeros,  we can proceed as follows

x² - 3x  + 2 = 0

Factoring that xpression

( x -1 ) * ( x - 2 ) = 0

Then either   x- 1  =  0   and    x₁ = 1        or

x  -  2  =  0      and       x₂  =  2