Question

Determine which of the following statements are true if Parabola 1 has the equation f(x)=x^2- 6x+8 and Parabola 2 has a leading coefficient of 1 and zeros at x= -6 and x=-2. Check all that apply.

a. Parabola 1 and Parabola 2 have the same line of symmetry.

b. Parabola 1 and Parabola 2 do not have a zero in common.

c. Parabola 1 crosses the y-axis higher than Parabola 2.

d. Parabola 1 has a lower minimum than Parabola 2.

Answer 1

x^2 - 6x + 8 = (x - 4)(x - 2) 
so the zeroes are 4 and 2 and the line of symmetry is x = 3
Parabola 2 has line of symmetry of x = -4 so a is not true.
and b is true ( no zeroes in common)
When x = 0 Parabola 1 has a y intercept of 8  
while Parabola 2 ( (x + 2)(x + 6) has y intercept of 2*6 = 12 so c is not true,
To find minimum va;lues
Parabola 1 vertex form = (x - 3)^2 - 9 + 8 = (x- 3)^2 - 1  So minimum is -1
Parabola 2 has minimum value of -4  so d not true

only b is true