Question$$f(x)=\frac{-5 x^{2}+10 x+40}{4 x^{2}-4 x-8}$$
Graph the following key features of $f(x)$ : 1) $y$-intercept 2) $x$-intercept(s) 3) vertical asymptote(s)

Studdy Solution
To find the vertical asymptotes, set the denominator equal to zero and solve for $x$:
$$4x^2 - 4x - 8 = 0$$
Divide the entire equation by $4$ to simplify:
$$x^2 - x - 2 = 0$$
Factor the quadratic equation:
$$(x - 2)(x + 1) = 0$$
Solve for $x$:
$$x - 2 = 0 \quad \Rightarrow \quad x = 2$$
$$x + 1 = 0 \quad \Rightarrow \quad x = -1$$
The vertical asymptotes are at $x = 2$ and $x = -1$.
The key features of the graph of $f(x)$ are: 1) $y$-intercept: $(0, -5)$ 2) $x$-intercepts: $(4, 0)$ and $(-2, 0)$ 3) Vertical asymptotes: $x = 2$ and $x = -1$