SOLUTION: f(x) = 7x2 - 2 how do I use the Quadratic Formula to find the x-intercepts of this equation?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: f(x) = 7x2 - 2 how do I use the Quadratic Formula to find the x-intercepts of this equation?      Log On


   

Question 210629: f(x) = 7x2 - 2 how do I use the Quadratic Formula to find the x-intercepts of this equation?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+7x%5E2+-+2 Start with the given function.


0+=+7x%5E2+-+2 Plug in f%28x%29=0


Notice that the quadratic 7x%5E2-2 is in the form of Ax%5E2%2BBx%2BC where A=7, B=0, and C=-2


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%287%29%28-2%29+%29%29%2F%282%287%29%29 Plug in A=7, B=0, and C=-2


x+=+%280+%2B-+sqrt%28+0-4%287%29%28-2%29+%29%29%2F%282%287%29%29 Square 0 to get 0.


x+=+%280+%2B-+sqrt%28+0--56+%29%29%2F%282%287%29%29 Multiply 4%287%29%28-2%29 to get -56


x+=+%280+%2B-+sqrt%28+0%2B56+%29%29%2F%282%287%29%29 Rewrite sqrt%280--56%29 as sqrt%280%2B56%29


x+=+%280+%2B-+sqrt%28+56+%29%29%2F%282%287%29%29 Add 0 to 56 to get 56


x+=+%280+%2B-+sqrt%28+56+%29%29%2F%2814%29 Multiply 2 and 7 to get 14.


x+=+%280+%2B-+2%2Asqrt%2814%29%29%2F%2814%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+sqrt%2814%29%2F7 or x+=+-sqrt%2814%29%2F7 Break up the expression and reduce.


So the solutions are x+=+sqrt%2814%29%2F7 or x+=+-sqrt%2814%29%2F7