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

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A quadratic equation is defined as having the form y = ax^2 + bx + c, where a is not equal to zero. Even if c = 0, resulting in y = ax^2 + bx, it remains a quadratic equation. Similarly, if b = 0, leading to y = ax^2, it is still classified as a quadratic equation due to the presence of the x^2 term. The key factor is that the coefficient a must not be zero for it to retain its quadratic classification. Thus, both cases of b = 0 and c = 0 still qualify as quadratic equations.
LearninDaMath
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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?
 
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LearninDaMath said:
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
LearninDaMath said:
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.
LearninDaMath said:
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?
 
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