How To Write A Quadratic Function In Factored Form With Given Zeros

a quadratic function has zeros at…

x=p and x=q

If a quadratic function has zeros at x = a and x = b, then it can be written in factored form as:

f(x) = a(x – a)(x – b)

This is because the roots or zeros of the function give us the factors of the quadratic equation. When we multiply out the factors, we get the quadratic equation back.

For example, suppose a quadratic function has zeros at x = 2 and x = 5. Then, we can write the function in factored form as:

f(x) = a(x – 2)(x – 5)

where a is a constant that determines the shape and orientation of the parabola. We can find the value of a by substituting a known point on the quadratic curve, such as the vertex, and solving for a.

It is important to note that a quadratic function may not have real roots or zeros in some cases. For instance, if the discriminant (b^2 – 4ac) is negative, the quadratic equation will have complex roots. In this case, we cannot factor the quadratic function with real coefficients.

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