Question

Which of the following quadratic functions has a graph that opens downward? Check all that apply. A v=Bx2- 8x– 13 B. v= - (3+x? e. v=zx2 - 13x+5 O d. v=2r-

Answer 1

Ok, so

Remember that:

For any quadratic equation of the form:

$y=ax^2+bx+c$

- If the leading coefficient is greater than zero, the parabola opens upward, and

- If the leading coefficient is less than zero, the parabola opens downward.

So, here we have the following functions:

$v=\frac{1}{3}x^2-8x-13$

The leading coefficient is greater than zero, so this parabola opens upward.

Option B:

$\begin{gathered} v=-(3+x^2) \\ v=-x^2-3 \end{gathered}$

The leading coefficient is less than zero, so this parabola opens downward.

Option C:

$v=\frac{2}{3}x^2-13x+5$

The leading coefficient is greater than zero, so this parabola opens upward.

Option D:

$v=2x-x^2$

The leading coefficient is less than zero, so this parabola opens downward.

Therefore, the correct options are B and D.