Question

One x-intercept for a parabola is at the point (2.5,0). Use the quadratic formula to find the other x-intercept for the parabola defined by this equation: y=2x^2-x-10

separate the values with a comma. Round, if necessary, to the nearest hundredth.

Answer 1

(-2, 0)

Explanation:

Focus on the given equation: y=2x^2-x-10. Here the coefficients are a = 2, b = -1 and c = -10.

Then the roots (closely related to x-intercepts) are

-b plus or minus sqrt(b^2 - 4ac)

x = ------------------------------------------------

2a

or, specifically for the problem at hand,

-(-1) plus or minus sqrt([-1]^2 - 4[2][-10]

x = -------------------------------------------------------- = 5/2 (same as 2.5 in (2.5,0) )

2[2]

1 plus or minus sqrt(81)

= ---------------------------------------

4

1 plus 9 1 minus 9

= ------------- or ------------------- => 10/4 or 5/2 OR -8/4 = - 2

4 4

One x-intercept is given: (2.5, 0).

The other is (-2, 0)