# Quadratic Function: Number of Zeros

How to find the number of zeros of a quadratic function by using its discriminant: formula, 3 examples, and their solutions.

## Formula

For a quadratic function

y = ax^{2} + bx + c

(a ≠ 0),

the discriminant D is

D = b^{2} - 4ac.

It's the same D of a quadratic equation.

The discriminant of a quadratic function

determines the number of zeros.

If D is plus,

then it has two zeros.

If D = 0,

then it has one zero.

If D is minus,

then it has no zeros.

(It doesn't meet with the x-axis.)

## Exampley = x^{2} + 8x - 3

The given quadratic function is

y = 1x^{2} + 8x - 3.

a = 1

b = +8

c = -3

Then D = 8^{2} - 4⋅1⋅(-3).

8^{2} = 64

-4⋅1⋅(-3) = +12

64 + 12 = 76

D = 76

D is plus.

So the quadratic function has

two zeros.

So

two zeros

is the answer.

## Exampley = -4x^{2} + 4x - 1

The given quadratic function is

y = -4x^{2} + 4x - 1.

a = -4

b = +4

c = -1

Then D = 4^{2} - 4⋅(-4)⋅(-1).

4^{2} = 16

-4⋅(-4)⋅(-1) = -16

16 - 16 = 0

D = 0

So the quadratic function has

one zero.

So

one zero

is the answer.

## Exampley = 2x^{2} - x + 7

The given quadratic function is

y = 2x^{2} - x + 7.

a = 2

b = -1

c = +7

Then D = (-1)^{2} - 4⋅2⋅7.

(-1)^{2} = 1

-4⋅2⋅7 = -56

1 - 56 = -55

D = -55

D is minus.

So the quadratic function has

no zeros.

So

no zeros

is the answer.