Question

1. how would you describe the end behavior of a quadratic function?

Explanation:

Step1: Recall quadratic function form

A quadratic function is $f(x)=ax^{2}+bx + c$, $a
eq0$.

Step2: Analyze when $a>0$

For $y = ax^{2}+bx + c$ with $a>0$, as $x
ightarrow\pm\infty$, $y
ightarrow+\infty$. The parabola opens upward.

Step3: Analyze when $a < 0$

For $y=ax^{2}+bx + c$ with $a < 0$, as $x
ightarrow\pm\infty$, $y
ightarrow-\infty$. The parabola opens downward.

Answer:

If the coefficient $a$ of $x^{2}$ in the quadratic function $y = ax^{2}+bx + c$ is positive, as $x$ approaches positive or negative infinity, $y$ approaches positive infinity. If $a$ is negative, as $x$ approaches positive or negative infinity, $y$ approaches negative infinity.