Question

consider the function (f(x) = -\frac{1}{4}x^2 - \frac{1}{2}x - \frac{5}{4})

what is the vertex of (f)?

what is the equation of the line of symmetry of (f)?

(f) has a maximum of

the (x)-intercept(s) of (f) is/are

the (y)-intercept of (f) is

Explanation:

⚡ Using what you learned: graphing quadratic functions

Step 1: Identify the y-intercept definition

The \(y\)-intercept of a function is the point where the graph crosses the \(y\)-axis, which occurs when \(x = 0\). To find it, evaluate \(f(0)\).

Step 2: Evaluate the function at x = 0

Substitute \(x = 0\) into the given function:

$$ f(x) = -\frac{1}{4}x^2 - \frac{1}{2}x - \frac{5}{4} $$

$$ f(0) = -\frac{1}{4}(0)^2 - \frac{1}{2}(0) - \frac{5}{4} $$

$$ f(0) = -\frac{5}{4} $$

The \(y\)-intercept is the point \((0, -\frac{5}{4})\), or simply the value \(-\frac{5}{4}\) (often written as \(-1.25\)).

Answer:

\(-\frac{5}{4}\) (or \((0, -\frac{5}{4})\))