Answer:
Option D is correct
Step-by-step explanation:
A quadratic equation is in the form of [tex]y =ax^2+bx+c[/tex] ....[1]
then;
the axis of symmetry is given by:
[tex]x = \frac{-b}{2a}[/tex]
Vertex = [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]
As per the statement:
Given the function:
[tex]y=f(x) =x^2-x-2[/tex] ....[2]
On comparing with [1] we have;
a = 1, b = -1 and c = -2
Then;
[tex]x =\frac{-(-1)}{2(1)} = \frac{1}{2}[/tex]
Substitute the value of x in f(x) we have;
[tex]f(\frac{1}{2}) = (\frac{1}{2})^2-\frac{1}{2}-2 = \frac{1}{4}-\frac{5}{2} = \frac{1-10}{4} = \frac{-9}{4}[/tex]
⇒[tex]f(\frac{1}{2}) = -2\frac{1}{4}[/tex]
Vertex =[tex](\frac{1}{2}, -2\frac{1}{4})[/tex]
x-intercept states that the graph crosses the x-axis.
From the graph, the function cuts the x-axis at:
x = -1 and x = 2
x-intercepts = (-1, 0) and (2, 0)
y-intercept states that the graph crosses the y-axis
From the given graph we have;
y = -2
y-intercept = (0, -2)
Therefore,
Vertex =[tex](\frac{1}{2}, -2\frac{1}{4})[/tex]
Axis of symmetry: [tex]x=\frac{1}{2}[/tex]
x-intercepts = (-1, 0) and (2, 0)
y-intercept = (0, -2)
