Is a Quadratic Equation with b=0 or c=0 Still a Quadratic?

[LearninDaMath]

A quadratic equation has the form y = ax^2 + bx + c. However, if c = 0, then y = ax^2 + bx. Is it still called a quadratic equation? And if b = 0 so that y = ax^2, is it still given the title of quadratic equation?

I would guess yes since it still has a power of 2 and is a parabola. Is this correct?

 

[Mark44]

A quadratic equation has the form y = ax^2 + bx + c.

What you're showing is a quadratic function. A quadratic equation in standard form looks like this:
ax² + bx + c = 0

However, if c = 0, then y = ax^2 + bx. Is it still called a quadratic equation?

ax² + bx = 0 is still a quadratic equation. The only restriction is that a $\neq$ 0.

And if b = 0 so that y = ax^2, is it still given the title of quadratic equation?

I would guess yes since it still has a power of 2 and is a parabola. Is this correct?