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I know how the coefficients in quadratic functions $y=ax^2+bx+c$ affect its graph, but how exactly does the coefficients in cubic functions $y=ax^3+bx^2+cx+d$ affect the final graph?

I've read this answer from Quora, but it did not really help me. My math level is Algebra 1, so is there an answer that would not exceed what I could comprehend?

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    Just as it's easier to interpret the constants in the representation $x \mapsto a (x - h)^2 + k$ of a quadratic function, it is in some ways easier to interpret the constants in the representation $x \mapsto a[(x - h)^3 + j(x - h)] + k$ for a cubic function. In particular, $a$ controls the asymptotic growth of the function (and its sign whether the function increases or decreases as $x$ gets large), $(h, k)$ is the point of symmetry of its graph, and $j$ is a parameter that controls the direction and strength of the "wobble" about the symmetry point: The function is injective iff $j \geq 0$. – 2017-02-23
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    As for quadratic functions, the number of real roots of a cubic function is controlled by the sign of its discriminant, which in this case is a rather complicated polynomial in $a, b, c, d$, but its expression in the factored representation is much simpler, $-a^2 (4 a^2 j^3 + 27 k^2)$. – 2017-02-23

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