The x-intercept is:
[tex]x=-3+\sqrt{26},\ x=-3-\sqrt{26}[/tex]
and y-intercept is:
[tex]y=-17[/tex]
x-intercept--
The x-intercept is the x-value of the point where the y-value is zero.
y-intercept--
The y-intercept is the y-value of the point where the x-value is zero.
The parabola is given by the equation:
[tex]y=x^2+6x-17[/tex]
when y=0
we have:
[tex]x^2+6x-17=0[/tex]
The solution of the quadratic equation of the type:
[tex]ax^2+bx+c=0[/tex]
is given by:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a=1, b= 6 and c= -17
Hence,
[tex]x=\dfrac{-6\pm \sqrt{6^2-4\times 17\times 1}}{2}\\\\x=\dfrac{-6\pm \sqrt{36+68}}{2}\\\\x=\dfrac{-6\pm \sqrt{104}}{2}[/tex]
[tex]x=-3+\sqrt{26},\ x=-3-\sqrt{26}[/tex]
Also, when x=0
we have:
[tex]y=-17[/tex]
Hence, the x-intercept is:
[tex]x=-3+\sqrt{26},\ x=-3-\sqrt{26}[/tex]
and y-intercept is:
[tex]y=-17[/tex]
