Finding the x-intercept?

Question

Hi everyone,

I have the problem y = 2x^2 -4x -9, and have to find the x-intercept.

@tony: Would you mind showing the other 2 processes?

Answer 1

The x-intercept is where the line crosses the x-axis (or in this case, where the parabola crosses the x-axis). This happens when y=0. So, first set y=0. Now, normally, you'd have 3 options for solving this (besides graphing). But, in this case, only 1 method will work to give you a precise answer. This method is the quadratic formula which is 'the opposite of b plus or minus the square root of (b squared minus 4ac) all over 2a; where a=2, b= -4, c=-9 (these being the coefficients of the first, second and third terms). Once you plug in this data, you get 1 plus or minus the square root of 22 over 2. Hope this helps!

Answer 2

Certainly, the quadratic formula gives the intercepts as
x = (2 +/- sqrt(22))/2.

By completing the square: we start with 2x^2 - 4x - 9 = 0. Write this in the form 2x^2 - 4x = 9, then 2(x^2 - 2x) = 9. Now we see that to complete the square inside the parens, we must add 1, so 2(x^2 - 2x + 1) = 9 + 2(1), or 2(x - 1)^2 = 11. Next we divide both sides by 2, then take square roots:
(x - 1)^2 = 11/2, and x - 1 = +/-sqrt(11/2). Thus, x = 1 +/- sqrt(11/2). (Notice that these roots agree with those found previously.)

Finally , factoring we have
(x - (1 + sqrt(11/2))(x - (1 - sqrt(11/2) = 0.

Answer 3

Make y zero and use the quadratic formula to get the two x-intercepts.

Answer 4

wow thats a tough question, im asian and even i dont know it.