Question

Find the x-intercepts for the parabola defined by the equation below.

y = 2x2 + 2x - 4

Answer 1

The parabola intercepts the x-axis happen when? Well, it's when "y" = 0. So you want to solve for x, 0 = 2x^2 + 2x -4

Answer 2

0 = 2x^2 + 2x -4 = (2x -2)(x + 2). So 2x -2 = 0 OR x+2=0 are the two solutions.

Answer 3

So in each case, solve for x, and those will be your answers.

Answer 4

Break it down a little more? Still confused

Answer 5

Ok. So by definition the x-intercept of a line/graph is when y=0 (since at that point will then be "on the x axis").

Answer 6

for example (1,0), (2,0), -3,0) etc... are all points that intercept the x-axis - as you can see if you graph them. That makes perfect sense, since the y-coordinate is 0.

Answer 7

So given the graph (in this case a parabola), will intercept the x-axis when the y coordinate is 0, go ahead and replace "y" with "0" in the initial equation and solve for x

Answer 8

0 = 2x^2 + 2x -4

Answer 9

when you see something like this (called a quadratic equation because it's in the form ax^2+bx+c =0), there are two ways to solve it

Answer 10

once is to use the quadratic formula - because in this format you know the values of a, b, and c http://en.wikipedia.org/wiki/Quadratic_equation

Answer 11

(which in this case are 2, 2, and -4)

Answer 12

The second way is to factor the equation. That is change it into 2 terms that are equivalent when multiplied together.

Answer 13

2x^2 + 2x -4 = (2x -2)(x + 2)

Answer 14

Now once it is factored, you'll notice something interesting about the right hand side

Answer 15

*anything* multiplied by zero is also zero - which is exactly what you want y to be. and hence just by factoring, you can also get both solutions.

Answer 16

when *either* 2x -2 = 0, OR x+2=0, you know the whole thing will be zero too (since something gets multipled by 0)

Answer 17

And so 2x-2 =0, so in that case x= 1. in the second case x+2 =0 , so x=-2. So you know that the parabola intercepts the x axis when x=1, or x=-2, so at (1,0) and (-2,0)