Question

one x-intercept for a parabola is at the point (2, 0). use the quadratic formula to find the other x-intercept for the parabola defined by y=x^2-3x+2​

Answer 1

Explanation:

There are 3 ways to find the other x intercept.

1) Polynomial Long Division.

Divide x^2 - 3x + 2 by the binomial x - 2, because by the Factor Theorem if a is a root of a polynomial then x - a is a factor of said polynomial.

2) Just solving for x when y = 0, by using the quadratic formula.

`x^2 - 3x + 2 = 0\\x_(12) = (3 \pm √(9 - 4(1)(2)))/(2) = (3 \pm 1)/(2) = 2, 1`.

So the other x - intercept is at (1, 0)

3) Using Vietta's Theorem regarding the solutions of a quadratic

Namely, the sum of the solutions of a quadratic equation is equal to the quotient between the negative coefficient of the linear term divided by the coefficient of the quadratic term.

`x_1 + x_2 = (-b)/(a)`

And the product between the solutions of a quadratic equation is just the quotient between the constant term and the coefficient of the quadratic term.

`x_1 \cdot x_2 = (c)/(a)`

These relations between the solutions give us a brief idea of what the solutions should be like.