Question

If the graph of $|y|=f\left(x\right),$ where $f\left(x\right)=a{x}^2+bx+c;b\&cϵR;a\ne 0,$ has the maximum vertical height 4, then

• A. $a>0$
• B. $a<0$
• C. $(b^2-4ac)$ is negative
• D. Nothing can be said

Answer 1

The correct option is B $a<0$

Given $:$ Graph of $|y|=f\left(x\right)$ , where $a{x}^2+bx+c$ has maximum vertical height 4

To find $:$ The condition of $a$

Solution $:$ All quadratic functions have a U-shaped graph called a parabola.

The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate denoted by $x=-\frac{b}{2a}$

The y-coordinate of the vertex is the maximum or minimum value of the function.

If the y-coordinate has maximum value then parabola opens down, and $a<0$