vertex = (3,- 5 )
given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then
the x-coordinate of the vertex is
= -
y = x² - 6x + 4 is in standard form
with a = 1, b = - 6 and c = 4, hence
= -
= 3
substitute this value into the equation for y- coordinate
y = 3² - 6(3) + 4 = 9 - 18 + 4 = - 5
vertex = (3, - 5 ) → second table
Answer:
A. between 3.0 and 3.5 and between 4.0 and 4.5
Step-by-step explanation:
The idea here is that if a function is continuous and you have points on opposite sides of the x-axis, then there must be a zero-crossing between those points. As the table and graph show, ...
... (3.0, 4.0) and (3.5, -0.2)
are points on opposite sides of the x-axis. So, there must be a zero crossing between x=3.0 and x=3.5.
Likewise, ...
... (4.0, -0.8) and (4.5, 0.1)
are points on opposite sides of the x-axis. So, there must be a zero-crossing between x=4.0 and x=4.5
The appropriate answer choice lists both of these possible zero crossings.
