SOLUTION: Find all intercepts for the graph of the quadratic function. f(x)=5x^2-38x+21

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find all intercepts for the graph of the quadratic function. f(x)=5x^2-38x+21      Log On


   

Question 130393: Find all intercepts for the graph of the quadratic function. f(x)=5x^2-38x+21
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the y-intercept. To do that, simply plug in x=0



f%28x%29=5x%5E2-38x%2B21 Start with the given function


f%280%29=5%280%29%5E2-38%280%29%2B21 Plug in x=0


f%280%29=5%2A0-38%2A0%2B21 Raise 0 to the 2nd power to get 0


f%280%29=0-38%2A0%2B21 Multiply 5 and 0 to get 0


f%280%29=0-0%2B21 Multiply 38 and 0 to get 0


f%280%29=0%2B21 Subtract 0 from 0 to get 0


f%280%29=21 Add 0 and 21 to get 21



So the y-intercept is (0,21)





Now let's find the x-intercept. To do that, simply plug in f%28x%29=0 (ie y=0)


f%28x%29=5x%5E2-38x%2B21 Start with the given function


0=5x%5E2-38x%2B21 Plug in f%28x%29=0




0=%28x-7%29%285x-3%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-7=0 or 5x-3=0

x=7 or x=3%2F5 Now solve for x in each case


So the x-intercepts are
and