Question 128351
First let's find the x-intercept(s)


{{{y=x^2-6x-7}}}  Start with the given equation


To find the x-intercept, let y=0


{{{0=x^2-6x-7}}} Plug in {{{y=0}}}




{{{0=(x-7)(x+1)}}} Factor the right side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x-7=0}}} or  {{{x+1=0}}} 


{{{x=7}}} or  {{{x=-1}}}    Now solve for x in each case



So the x-intercepts are (-1,0) and (7,0)




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Now let's find the y-intercept


{{{y=x^2-6x-7}}}  Start with the given equation


To find the y-intercept, let x=0




{{{f(0)=1(0)^2-6(0)-7}}} Plug in {{{x=0}}}



{{{f(0)=1*0-6*0-7}}} Raise 0 to the 2nd power to get 0



{{{f(0)=0-6*0-7}}} Multiply 1 and 0 to get 0



{{{f(0)=0-0-7}}} Multiply 6 and 0 to get 0



{{{f(0)=0-7}}} Subtract 0 from 0 to get 0



{{{f(0)=-7}}} Subtract 7 from 0 to get -7



So when {{{x=0}}}, we have {{{y=-7}}}



So the y-intercept is (0,-7)




If we graph the parabola, we get



{{{ graph( 500, 500, -10, 10, -10, 10, x^2-6x-7) }}} Graph of {{{y=x^2-6x-7}}} 



We can see that the x-intercepts are (-1,0) and (7,0) and that the y-intercept is (0,-7). So this verifies our answer.