# Thread: help me with function notation and other

1. ## help me with function notation and other

Q1) For the function g(x)=x²-4x
Find in the simplest form g(a+1)

Q2) Find the equation of the line joining: (3,4) and (5,-3)

Q3) Factorise: 4t²-1

Q4) Solve: 3x²-x-5=0

Thanks

2. are these homework problems?

Originally Posted by greenbean
Q1) For the function g(x)=x²-4x
Find in the simplest form g(a+1)
write as x(x - 4)

now replace x with (a + 1) and simplify

Q2) Find the equation of the line joining: (3,4) and (5,-3)
the slope of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ are given by: $m = \frac {y_2 - y_1}{x_2 - x_1}$

the equation of a line is of the form $y = mx + b$

you can find m using the above formula and then use one of the coordinates as the values of x and y. plug them in the equation of the line along with m and solve for b. or, if you prefer, you can use the point slope form: $y - y_1 = m(x - x_1)$. this gives the equation of the line with slope $m$ passing through the point $(x_1,y_1)$

Q3) Factorise: 4t²-1
write as (2t)^2 - 1

this is the difference of two squares. factor accordingly

Q4) Solve: 3x²-x-5=0
use the quadratic formula. you do remember it, right?

3. thanks!