Question

1.
The graph of the function y = x +x-6 drawn below.
y
-> X
A
A
B
С
(b)
(c)
Write down the coordinates of the point C.
Calculate the coordinates of the points A and B.
Calculate the coordinates of the minimum.

Answer 1

Answer:  See below

Step-by-step explanation:

A.  Point C is the y-intercept, the value of y when x = 0.  We know x = 0 for this point, (0,?).  To find y, wither find it on the graph (y = -6) or calculate it with the equation:

y = $x^{2}$ +x-6

For x = 0, y becomes -6

Point C is (0,-6)

B.   Y is zero at both points A and B.  We want the values of x that will make the equation equal to zero.  We can read them from a graph (where the line crosses the x axis), or factor the equation and set each factor to zero:

y = $x^{2}$ +x-6

y = (x + 3)(x - 2)

For y to be zero, either  (x + 3) or (x - 2) must equal zero.  That would occur for bot x = -3 and x = 2.

The points A and B are therefore:  

A (-3,0)

 B  (2,0)

We can find the minimum of this function by taking the first derivative and setting it equal to zero, the point at which the slope of the line is zero.

y = $x^{2}$ +x-6

y' = 2x + 1

2x = -1

x = -(1/2)

At x = - 1/2, y becomes -6.25

The minimum is (-(1/2), - 6.25)

See the attachment.