Explain how to show that a quadratic equation contains a perfect square trinomial.

Answer 1

To show that a quadratic equation contains a perfect square trinomial, we need to factor the quadratic equation into the form of (ax + b)^2, where a and b are constants.

Here are the steps to show that a quadratic equation contains a perfect square trinomial:

1. Write the quadratic equation in standard form: ax^2 + bx + c = 0.

2. Check if the quadratic equation is in the form of (ax + b)^2. To do this, find the discriminant (b^2 - 4ac) of the equation. If the discriminant is a perfect square, then the quadratic equation can be factored into a perfect square trinomial.

3. If the discriminant is a perfect square, then factor the quadratic equation into (ax + b)^2. This will show that the quadratic equation contains a perfect square trinomial.

For example, if the quadratic equation is x^2 + 4x + 4 = 0, we can rewrite it as (x + 2)^2 = 0. In this case, the quadratic equation contains a perfect square trinomial.