Question

State the following statement is True or False

If a quadratic function $f\left(x\right)=a{x}^2+bx+c$ has a downward parabola then $a>0$.

• A. True
• B. False

Answer 1

The correct option is B False

$y=a{x}^2+bx+c$

$\therefore y=a(x^2+\frac{b}{a}x+\frac{c}{a})$

$\therefore y=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2}+\frac{c}{a}-\frac{b^2}{4a^2})$

$\therefore (y-(c-\frac{b^2}{4a}\left)\right)=a(x+\frac{b}{2a}{)}^2$

For $a>0$, this is an upward opening parabola

So, the statement is false.