Question

Solve graphically...........

Answer 1

The answer by graphical representation are given below. All the 1 graphs are attached with the question in top of them

Answer 2

1.

x = -1 or x = -1.75

2.

x = 1 or x = 1/3

3.

No solution

4.

x = 1

5.

x = -1

6.

x = 1/2

7.

x = -1/2

8.

x = -1.45 or x = 1.25

9.

x = -3 or x = 4

10.

x = 4

11.

x = -2 or x = 7

12.

x = -13 or x = 8

13.

x = -2 or x = 2.25

14.

x = -3.27 or x = 4.27

15.

x = 2 or x = -2

Explanation:

To solve a quadratic equation graphically we simply graph the function and note the points where the function intersects with the x-axis (the line y =0).

Consider the quadratic equation in number 11;

`x^(2) -5x-14=0`

In order to solve the equation graphically we plot the function;

`y=x^(2) -5x-14`

The x-coordinate(s) of the point(s) where this function intersects with the x-axis will be the solution to the original quadratic equation;

We can use technology to plot the function as shown by the attachment below;

The function
`y=x^(2) -5x-14` crosses the line y = 0 (x-axis) at the points; x = -2 and x = 7.

The solutions to the given quadratic equation are thus;

x = -2 or x = 7

Lastly, if the plotted function does not intersect with the x-axis then the original quadratic equation has no roots or solutions;

This applies to question 3 as seen from the second attachment below;