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An example of quadratic equation with this behavior is:
[tex]y = x^2 + x + 20[/tex]
Which is sketched at the end of this answer.
A quadratic equation has the format:
[tex]y = ax^2 + bx + c[/tex]
It's roots are given by:
[tex]\frac{-b \pm \sqrt{\Delta}}{2}[/tex]
The number of roots depends on the discriminant [tex]\Delta = b^2 - 4ac[/tex], that is:
In this problem, it will have only positive y-values if: [tex]\Delta < 0[/tex] and [tex]c > 0[/tex]
Thus, an example is:
[tex]y = x^2 + x + 20[/tex]
Which is sketched below.
A similar problem is given at https://brainly.com/question/19776811
