Answer:
(0, -5) and (2, -8.75)
Explanations
Given the function expressed as:
[tex]g(x)=(x-2)^2-9[/tex]
We are to find two other coordinates other than the vertex and x-intercept. Note that the equation of a parabola in vertex form is expressed as:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]
Another coordinate point is the y-intercept of the graph. The y-intercept occurs at the point where x = 0.
Substitute x = 0 into the given function;
[tex]\begin{gathered} g(x)=(x-2)^2-9 \\ g(0)=(0-2)^2-9 \\ g(0)=(-2)^2-9 \\ g(0)=4-9 \\ g(0)=-5 \end{gathered}[/tex]
Hence the y-intercept of the graph is (0, -5)
The other coordinate of the function we can determine is the FOCUS.
The coordinates for the focus of the parabola is given as (h, k+1/4a).
where:
• a is the intercept
,
• (h, k) is the vertex
Comparing the given function with the general function, we can see that:
a = 1
h = 2
k = -9
Substitute these values into the coordinate of the focus will give:
[tex]\begin{gathered} \text{Focus}=(h,k+\frac{1}{4a}) \\ \text{Focus}=(2,-9+\frac{1}{4(1)}) \\ \text{Focus}=(2,\frac{-36+1}{4}) \\ \text{Focus}=(2,-8.75) \end{gathered}[/tex]
Therefore the other two points on the graph are (0, -5) and (2, -8.75)
