**Solutions to Math Assignment **

**Q1: ** P=(x,y) is a point in

(a) To obtain a function in terms of x that gives the distance between P and point (1,0)

We know that, then

Therefore, the function that calculates the distance between P and the point (1,0) is:

(b) The smallest distance between the two points.

Here we are required to solve the polynomial inside the square root sign.

This is the same as.

Solving for x

Therefore the values of x are,

The value of x that gives the shortest distance is

**Q2:**

(a) In this experiment the independent variable is Absence and the dependent variable is Final Grade.

(d) Finding the equation of the line

First we obtain the gradient using two points say, (2,87) and (0, 93).

We will take one point in the line i.e. (2, 87) and an arbitrary point (x, y)

(e) In our equation, we have obtained the gradient to be -3. This means that there is a negative correlation between the variables that we have. In simple terms, it means that the more the number of absence the lower the performance.

(f) 4 absences

**Q3:**

(a) The graph of opens downwards.

(b) The vertex and axis of symmetry

To obtain the coordinates of the vertex we do the following:

To obtain b we substitute the value of x in the equation:

Therefore the coordinates of the vertex are

The axis of symmetry is given by, this means that it is

(c) To find the x-intercept and y-intercept in this equation we let f(x) be equal to zero

Solving it to obtain the values of x

These are the x-intercepts