Which point is an $$ x $$-intercept of the quadratic function $$ f(x)=(x-8)(x+9) $$ ? $$ (0,8) $$ $$ (0,-8) $$ $$ (9,0) $$ $$ (-9,0) $$

Question

UpStudy AI · Accepted Answer

1. An $$ x $$-intercept occurs when $$ f(x) = 0 $$.

2. Given the quadratic function $$ f(x) = (x-8)(x+9) $$, set it equal to zero:
   $$
   (x-8)(x+9) = 0
   $$

3. By the Zero Product Property, either
   $$
   x - 8 = 0 \quad \text{or} \quad x + 9 = 0.
   $$

4. Solving each equation:
   $$
   x - 8 = 0 \quad \Longrightarrow \quad x = 8
   $$
   $$
   x + 9 = 0 \quad \Longrightarrow \quad x = -9.
   $$

5. The $$ x $$-intercepts are at the points $$ (8, 0) $$ and $$ (-9, 0) $$.

6. Among the provided options, the point $$ (-9, 0) $$ is an $$ x $$-intercept of the function.

Thus, the correct answer is $$ (-9,0) $$.
The $$ x $$-intercept is at $$ (-9, 0) $$.

Which point is an \( x \)-intercept of the quadratic function \( f(x)=(x-8)(x+9) \) ? \( (0,8) \) \( (0,-8) \) \( (9,0) \) \( (-9,0) \)