Why the x-intercepts of a quadratic function are the solution to the quadratic equation?

Question

Pls answer this quick....................10 pts.................

Answer 1

It is notable that the x-intercepts, or solution, of a quadratic equation are known as the ROOTS or the ZEROS of that particular equation.

When you solve a quadratic equation, you are looking for the points that make the equation 0; recall that all problems have one side set to zero. For example:

x^2 + 2x + 1 = 0, the original being y=x^2 + 2x + 1

What you do when you solve the problem is look for the input values of x that give a y value of 0. It is precisely this that produces the effect of a solution being an x-intercept. Continuing:

(x+1)(x+1) = 0, x = -1

What you have done was assume that y=0 (and hence restricted yourself to the x-axis), then tried to find the x points where this
occurs. By setting y=0, you are "searching" along the x-axis; the ssolution is given where the function CROSSES the axis.

Answer 2

The x-intercepts of a quadratic function are the solutions to the quadratic function when the y value is equal to 0.
ax^2+bx+c=y the x-intercepts are when
ax^2+bx+c=0