Question

an artist is painting an amphitheater on a grid canvas. the equations below represent a curved seat section and the stage on the painting. at what points will the stage and seating intersect? select all that apply.\\(f(x) = -3\\)\\(f(x) = -(x - 3)^2 + 6\\)

Explanation:

Step1: Set equations equal

$-3 = -(x - 3)^2 + 6$

Step2: Isolate squared term

$(x - 3)^2 = 6 + 3$
$(x - 3)^2 = 9$

Step3: Solve for x

$x - 3 = \pm\sqrt{9}$
$x - 3 = 3$ or $x - 3 = -3$
$x = 6$ or $x = 0$

Step4: Find intersection points

For $x=0$, $f(x)=-3$; for $x=6$, $f(x)=-3$.

Answer:

$(0, -3)$ and $(6, -3)$