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

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SUMMARY

A quadratic equation retains its classification regardless of whether the coefficients b or c are zero. The standard form of a quadratic equation is expressed as y = ax^2 + bx + c, where a must not equal zero. If c = 0, the equation simplifies to y = ax^2 + bx, and if b = 0, it becomes y = ax^2. Both forms are still considered quadratic equations due to the presence of the x^2 term, confirming that they represent parabolic functions.

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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 [itex]\neq[/itex] 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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