Question

unit algebra: concepts and connections - aaa07 quadratic functions: standard form the ( a ) value of a function in the form ( f(x) = ax^2 + bx + c ) is negative. which statement must be true? the ( x )-intercepts are negative. the vertex is a maximum. the ( y )-intercept is negative. the axis of symmetry is to the left of zero.

Explanation:

Step1: Analyze vertex nature

For quadratic $f(x)=ax^2+bx+c$, if $a<0$, the parabola opens downward, so the vertex is the highest point (maximum).

Step2: Check other options

• y-intercept is $f(0)=c$, sign of $c$ is not given, so it can be positive/zero/negative.
• x-intercepts depend on discriminant $b^2-4ac$; they could be positive/negative/non-existent.
• Axis of symmetry is $x=-\frac{b}{2a}$; sign depends on $b$, which is not specified, so it can be left/right of zero.

Answer:

The vertex is a maximum.