Jenifer L. answered • 02/07/19
Math doesn't have to be hard!
When something crosses something else, for example Street A crosses Street B, we say it intersects it - Street A intersects Street B, or would it commonly referred to as the intersection of Street and Street B when giving directions. Likewise, the x-intercept crosses the x-axis. Therefore if we find the x-intercept we will find the values where it crosses the x-axis.
By definition, the x-intercept occurs when y=0 (same as f(x)=0, or in this case being written as y(x), which is all the same as y). We can find the x-intercept(s) by plugging in 0 for y, or in this case the same as y(x), and solving for x.
y(x) = 2x^2 - 50
0 = 2x^2 - 5 We need to get X by itself. First we can factor out a 2.
0 = 2(x^2 - 25) Divide both sides by 2.
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2 2
0 = x^2 - 25 Remember 0 divided by anything is 0.
0 = (x + 5)(x - 5) x^2 - 25 is the difference of squares, which difference of squares (x^2 - #, when # is a
perfect square, like 4, 9, 16, 25, 36, 64, etc) is always factored as (x + #)(x - #)
x + 5 = 0 & x -5 = 0 Once factored, set each piece equal to zero then solve for x.
x = -5 x = 5 Therefore the given function crosses the x-axis at x = -5 & x = 5
**Sorry, I have added spacing to make it easier to read a couple of times, but it keeps removing the formatting.
