Functions, Help?
1 Answer
(i)
(ii)
(iii)
Explanation:
(i)
When
Subtract
Factor,
Graph,
graph{2x^2-3x-9 [-5, 5, -15, 15]}
From the graph,
(ii)
Factor,
Perform complete the square method,
Let us recap our concepts,
color(red)(a^2)+color(green)(2ab)+color(blue)(b^2)=color(purple)((a+b)^2 Let
a=x and2ab=-3/2x
b=-(3/2x)/(2x)
color(white)(b)=-3/4 Now we have to add in
color(blue)((-3/4)^2) somehow,
2(color(red)(x^2)-color(green)(3/2x)+color(blue)((-3/4)^2)-(-3/4)^2) By adding and subtracting, I have not affected the original equation,
2(color(red)(x^2)-color(green)(3/2x)+cancel(color(blue)((-3/4)^2))-cancel((-3/4)^2))
=2(x^2-3/2x) Now simplify,
2(color(red)(x^2)-color(green)(3/2x)+color(blue)((-3/4)^2))-2(-3/4)^2 Make the perfect square and simplify,
2color(purple)((x-3/4)^2)-9/8
Hence,
The vertex formula is as follows:
By comparison, find the coordinates,
(iii)
Substitute,
When
Expand,
Apply discriminant, where
Simplify,
Add
Solve,