Answer
The point of intersection is $(-4, 68)$.
Work Step by Step
We want to find when $f(x) = g(x)$, so we set the two expressions equal to one another and solve:
$4(x^2 + 1) = 4x^2 - 3x - 8$
Use the distributive property:
$4x^2 + 4 = 4x^2 - 3x - 8$
Move all terms to the left side of the equation:
$3x + 12 = 0$
Factor out the GCF:
$3(x + 4) = 0$
Divide both sides by $3$:
$x + 4 = 0$
Subtract $4$ from each side of the equation:
$x = -4$
We can now plug this value into either $f(x)$ or $g(x)$ to find the corresponding value of $y$.
Let us use $f(x)$:
$f(x) = 4[(-4)^2 + 1]$
Evaluate exponents first:
$f(x) = 4(16 + 1)$
Simplify what is in parentheses:
$f(x) = 4(17)$
Multiply to simplify:
$f(x) = 68$
The point of intersection is $(-4, 68)$.
