Question 235891: For a quadratic function, how do you find the x-intercept(s)
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! To find the y-intercept, set x = 0 and solve for y.
To find the x-intercept, set y = 0 and solve for x.
Sample:
Given the function f(x) = -2x^2 - 5x + 4, find the intercepts.
Let x = 0 and solve for y.
f(0) = -2(0)^2 - 5(0) + 4
f(0) = 0 + 0 + 4
f(0) = 4
The y-intercept is the point (0,4).
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Now, let y = 0 and solve for x.
Keep in mind that y = f(x). So, set f(x) = 0 and solve for x.
0 = -2x^2 - 5x + 4
2x^2 + 5x - 4 = 0
This quadratic only factors using the quadratic formula.
After doing the math, I got:
x = (-5 ± √57)/4
So, the x-intercepts are the points ((-5 +√57)/4), 0) and ((-5 -√57)/4), 0).
The reason I got this odd-looking x value is because the function I selected did not factor other than using the quadratic formula.
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