Given the quadratic equation y = ax² + bx + c, let's evaluate each sentence.
(a) The y-intercept is the point (0, c).
The y-intercept is a point (0, y). Substituting x by 0, we have:
[tex]\begin{gathered} y=a*0+b*0+c \\ y=c \end{gathered}[/tex]
So, the y-intercept is the point (0, c).
The statement is TRUE
(b) The graph as a x-intercept (c, 0).
The x-intercept is the point (x, 0). Substituting y by 0, we have:
[tex]\begin{gathered} y=ax^2+bx+c \\ 0=ax^2+bx+c \end{gathered}[/tex]
So, the statement is FALSE.
(c) When a < , the function opens downtown.
When a < 0, the graph is:
So, the statement is TRUE.
(d) The graph has two x-intercepts.
The graph can have 0, 1 or 2 y-intercepts.
So, the statement is FALSE.
(e) If b = 0, then the vertex is on the x-axis.
When b = 0, then the vertex is on the x-axis. TRUE.
