The Process of Finding Zeroes of a Quadratic Function | Explained with an Example

Zeroes of a Quadratic Function

The zeroes of a quadratic function are the values of the independent variable (typically denoted by “x”) for which the function evaluates to zero

The zeroes of a quadratic function are the values of the independent variable (typically denoted by “x”) for which the function evaluates to zero. In other words, they represent the x-values at which the quadratic function crosses or intersects the x-axis.

Mathematically, a quadratic function can be expressed in the form of:

f(x) = ax^2 + bx + c

where “a,” “b,” and “c” are constants.

To find the zeroes of a quadratic function, you set the function equal to zero and solve the resulting equation, typically using factoring or the quadratic formula.

Let’s go through an example to illustrate the process. Consider the quadratic function:

f(x) = 2x^2 – 5x + 3

To find the zeroes, we set f(x) to zero:

2x^2 – 5x + 3 = 0

Now, we can solve this equation either by factoring or by using the quadratic formula. Let’s solve it using factoring.

First, we need to factor the quadratic expression:

(2x – 3)(x – 1) = 0

Now, we can apply the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero. Therefore, we can set each factor to zero:

2x – 3 = 0 or x – 1 = 0

Solving these equations, we find:

2x = 3 or x = 1

Dividing both sides of the first equation by 2:

x = 3/2

So, the zeroes of the quadratic function f(x) = 2x^2 – 5x + 3 are x = 3/2 and x = 1.

These are the x-values where the graph of the quadratic function intersects the x-axis.

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