Respuesta :
The parabola has only one x - intercept when k =20.
What is x-intercept?
The x intercept for any curve is the value of the x coordinate of the point where the graph cuts the x-axis.
When the parabola has only one intercept?
If the value of the discriminant is zero, there is one real solution for x. Then the parabola has only one x-intercept.
According to the given question
We have a equation of parabola
[tex]y = x^{2} + kx + 100[/tex]
The above parabola has only one x-intercept if the discriminant is zero.
⇒ [tex]k^{2} -4(1)(100) =0[/tex]
⇒ [tex]k^{2} = 400[/tex]
⇒[tex]k =\sqrt{400}[/tex]
⇒ k = 20
⇒ k = 20
Hence, the parabola has only one x - intercept when k =20.
Learn more about x-intercept here:
https://brainly.com/question/14180189
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