Question

2

The graphs of y = 3x² + 7x - 4 andy + 2x = 10 intersect at the points A and B.
Find the coordinates of A and B.
You must show all your working and give your answers correct to two decimal places.

Answer 1

(1.13, 7.74) and (-4.13, 18.26)

Explanation:

This can be solved in two ways: mathematically and graphically.

Graphing

Plot both lines and find where they intersect. See the attachment.

The intersection points are (1.13, 7.74) and (-4.13, 18.26)

Mathematical

y + 2x = 10

y = 10 - 2x

y = 3x² + 7x - 4

10 - 2x = 3x² + 7x - 4

3x² + 9x - 14 = 0

Solve this using the quadratic equation:

x = 1.13 and -4.13

Use these two values of x to find y:

y = 10 - 2x

y = 10 - 2(1.13)

y = 7.74

y = 10 -2x

y = 10 -2(-4.13)

y = 18.26

The two points are:

(1.13, 7.74) and (-4.13, 18.26)