Question

Give an example of a quadratic equation that has two real solutions. Give an example of a quadratic equation that has only one real solution. Give an example of a quadratic equation that has no real solutions. Explain how you know...

Answer 1

What is factored form?

Factored form is a form of a quadratic equation where it is written as y = a(x-p)(x-q), and p and q are both x-intercepts, or the solutions, roots, whatever you call them. In this case, we need one with two real solutions, so we can just make one of the quadratics in factored form with 2 integers as the points:

so we could do y = (x-2)(x+4) or anything in that nature.

A quadratic with no solutions is a quadratic with the vertex above the x-intercept and facing up. Since you know what vertex form already is, we can use that.

So, if the y-int has to be above the x-axis, it can be any positive value, but the a value has to remain positive:

y = 3(x-5)^2 +100

Something like that!

A quadratic with one solution has to have its vertex on the line. This way, there cannot be any x-intercepts, and it doesn't matter which way it's facing. This means that there is no y-intercept other than 0.

An example could be:

y = 3(x-4)^2

Since there is no y-value the value will stay on the x-intercept, only allowing one solution!

hope this helps!

Answer 2

A quadratic equation is a second-order polynomial equation in one variable with the general form ax^2 + bx + c = 0. An example of a quadratic equation that has two real solutions is x^2 - 5x + 6 = 0. An example of a quadratic equation that has only one real solution is x^2 + 4x + 4 = 0. An example of a quadratic equation that has no real solutions is x^2 + 4 = 0.

Step-by-step explanation:

A quadratic equation is a second-order polynomial equation in one variable with the general form ax^2 + bx + c = 0, where a, b, and c are constants.

An example of a quadratic equation that has two real solutions is x^2 - 5x + 6 = 0. The solutions to this equation are x = 2 and x = 3.

An example of a quadratic equation that has only one real solution is x^2 + 4x + 4 = 0. The solution to this equation is x = -2.

An example of a quadratic equation that has no real solutions is x^2 + 4 = 0. Since this equation has no real solutions, it does not intersect the x-axis.