SOLUTION: Use the quadratic formula to find the x-intercepts for the parabola f(x)=2x^2+11x-6?

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Question 289027: Use the quadratic formula to find the x-intercepts for the parabola f(x)=2x^2+11x-6?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2x%5E2%2B11x-6 Start with the given function.


0=2x%5E2%2B11x-6 Plug in f%28x%29=0


2x%5E2%2B11x-6=0 Rearrange the equation.


Now let's use the quadratic formula to solve for 'x'.

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 2%2Ax%5E2%2B11%2Ax-6=0 ( notice a=2, b=11, and c=-6)





x+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A2%2A-6+%29%29%2F%282%2A2%29 Plug in a=2, b=11, and c=-6




x+=+%28-11+%2B-+sqrt%28+121-4%2A2%2A-6+%29%29%2F%282%2A2%29 Square 11 to get 121




x+=+%28-11+%2B-+sqrt%28+121%2B48+%29%29%2F%282%2A2%29 Multiply -4%2A-6%2A2 to get 48




x+=+%28-11+%2B-+sqrt%28+169+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-11+%2B-+13%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-11+%2B-+13%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%28-11+%2B+13%29%2F4 or x+=+%28-11+-+13%29%2F4


Lets look at the first part:


x=%28-11+%2B+13%29%2F4


x=2%2F4 Add the terms in the numerator

x=1%2F2 Divide


So one answer is

x=1%2F2




Now lets look at the second part:


x=%28-11+-+13%29%2F4


x=-24%2F4 Subtract the terms in the numerator

x=-6 Divide


So another answer is

x=-6


So our solutions are:

x=1%2F2 or x=-6





Since the solutions are x=-6 or x=1%2F2, this means that the x-intercepts are and