Question

if the graph of a quadratic function intersects with the x axis two times, how many solutions are there to the equation when set equal to zero

Answer 1

Hello there!

This is a conceptual question about quadratic functions.

Remember that a solution of ANY function is where it intersects the x-axis, so if the quadratic function intersects the x-axis TWO times, this means that there are TWO real solutions.

Here's a list of things to remember that will help you out for quadratic functions...
•if a quadratic function intersects the x-axis twice, it has two real solutions.
•if a quadratic function intersects the x-axis once, it has one real solution and one imaginary solution.
•if a quadratic function intersects the x-axis zero times, it has zero deal solutions and two imaginary solutions.


Please NOTE: If you want to know how many solutions a polynomial function has, look at it's highest exponent. If it is 2, then it has 2 solutions whether they be real or imaginary. If it is 3, then it has 3 solutions.

Also, if one of the factors are the same for a polynomial function, the way it hits the x-axis changes! This is just some extra information to help you in the long run!


I hope this helps!
Best wishes :)