Question

Find the x-intercepts for the parabola defined by the equation below. y = x2 - 9x + 18

A. (-3, 0) and (-6, 0)


B. (0, -3) and (0, -6)


C. (0, 3) and (0, 6)


D. (3, 0) and (6, 0)

Answer 1

(3, 0) and (6, 0)

Explanation:

Find the x-intercepts for the parabola is equivalent to solve y = x^2 - 9x + 18 = 0. To do that, quadratic formula is used:

`x = (-b \pm √(b^2 -4(a)(c)))/(2(a))`

`x = (-(-9) \pm √((-9)^2 -4(1)(18)))/(2(1))`

`x = (9 \pm √(9))/(2)`

`x_1 = (9 + 3)/(2)`

`x_1 = 6`

`x_1 = (9 - 3)/(2)`

`x_2 = 3`

Then, the coordinates are (3, 0) and (6, 0)

Answer 2

Option D is the correct answer

Explanation:

The x intercepts of the parabola are the solutions of the equation. These points can be determined either by graphical method or by solving the quadratic equation with any of the methods of solving a quadratic equation.

In order to use the graphical method, values of x are picked and substituted into the equation to get corresponding values of y. The y values are plotted against the x axis and the parabola (downward) is drawn. The points where it cuts the horizontal axis become the solutions of the equation

y = x^2 - 9x + 18

Solving the equation by using the factorization method,

x^2 - 9x + 18 = 0

x^2 - 6x - 3x + 18 = 0

x(x-6)-3(x-6)

(x-6)(x-3) = 0

x -6 = 0 or x -3 = 0

x = 6 or x = 3

The x-intercepts are (3, 0) and (6, 0)