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WHAT IS A 2ND DEGREE POLYNOMIAL FUNCTION WHOSE GRAPH HAS ONLY POSITIVE Y-VALUES

Sagot :

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:

  • If [tex]\Delta > 0[/tex], it has two different real roots.
  • If [tex]\Delta = 0[/tex], it has one real root.
  • If [tex]\Delta < 0[/tex], it has no real roots.

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

View image Joaobezerra
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