Question

y = x² - 2x - 5\
y = x³ - 2x² - 5x - 9\
when the two equations shown are graphed in the coordinate plane, they intersect at a point.\
what is the y - coordinate of the point of intersection?\
enter your answer in the box.\
y = \boxed{}

Explanation:

Step1: Set equations equal

$x^2 - 2x - 5 = x^3 - 2x^2 - 5x - 9$

Step2: Rearrange to standard form

$x^3 - 3x^2 - 3x - 4 = 0$

Step3: Factor the cubic equation

$(x-4)(x^2+x+1)=0$

Step4: Solve for x-values

Real solution: $x=4$ (the quadratic has no real roots)

Step5: Find y using $x=4$

$y=(4)^2 - 2(4) - 5$
$y=16 - 8 - 5$

Answer:

$3$