the a value of a function in the form f(x) = ax² + bx + c is negative. which statement must be true?\nthe…
the a value of a function in the form f(x) = ax² + bx + c is negative. which statement must be true?\nthe vertex is a maximum.\nthe y - intercept is negative.\nthe x - intercepts are negative.\nthe axis of symmetry is to the left of zero.
Answer
Explanation:
Step1: Recall parabola properties
For a quadratic function $y = ax^{2}+bx + c$, the sign of $a$ determines the parabola's opening.
Step2: Analyze when $a<0$
If $a<0$, the parabola opens down - ward. For a downward - opening parabola, the vertex represents the highest point of the function, so it is a maximum.
Step3: Analyze other options
The $y$ - intercept is $f(0)=c$, and we have no information about $c$, so we can't say it's negative. The $x$ - intercepts are found by solving $ax^{2}+bx + c = 0$, and their signs depend on $b$ and $c$ as well as $a$. The axis of symmetry is $x=-\frac{b}{2a}$, and its position relative to zero depends on the sign of $b$ and $a$.
Answer:
The vertex is a maximum.