# Finding roots by factorising

If a quadratic equation can be factorised, the factors can be used to find the roots of the equation.

### Example

The equation factorises to give so the solutions to the equation are and .

The graph of crosses the x-axis at and .

### Example

The equation factorises to give so there is just one solution to the equation, .

The graph of touches the x-axis at .

### Example

.

Using the quadratic formula to try to solve this equation, , and which gives:

.

It is not possible to find the square root of a negative number, so the equation has no solutions.

The graph of does not cross or touch the x-axis so the equation has no roots.

### Finding the y-intercept

The graph of the quadratic equation crosses the y-axis at the point . The x-coordinate of any point on the y-axis has the value of 0 and substituting into the equation gives .

Question

Find the y-intercept of the following quadratic functions:

a)

b)

c)

a) The constant term is -2, so the y-intercept is (0, -2)

b) The constant term is 17, so the y-intercept is (0, 17)

c) The constant term is 0, so the y-intercept is (0, 0)