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

In summary, a quadratic equation has the form ax^2 + bx + c = 0, and if c = 0 or b = 0, it is still considered a quadratic equation as long as a \neq 0. This is because it still has a power of 2 and forms a parabola.
  • #1
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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  • #2
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?
 

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

Is a quadratic equation still considered quadratic if the coefficient of the x term (b) is equal to 0?

Yes, a quadratic equation is still considered quadratic even if the coefficient of the x term is 0. This is because a quadratic equation is defined as an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a must be non-zero. As long as the equation follows this form, it is considered quadratic.

Can a quadratic equation have a coefficient of 0 for the constant term (c)?

Yes, a quadratic equation can have a coefficient of 0 for the constant term. This means that the equation will have the form ax^2 + bx = 0, where a and b are non-zero constants. This type of quadratic equation is called an incomplete quadratic equation.

What is the significance of the coefficient of the x term (b) being equal to 0 in a quadratic equation?

The coefficient of the x term (b) determines the shape of the quadratic curve. When b=0, the curve will be a vertical line passing through the origin. This type of quadratic equation is called a pure quadratic equation and it has only one solution, which is x=0.

How do you graph a quadratic equation with b=0 or c=0?

When b=0, you can graph the quadratic equation by plotting the y-intercept (c) and drawing a vertical line through that point. When c=0, you can graph the quadratic equation by finding the x-intercepts (solutions) and plotting them on the x-axis. If the x-intercepts are imaginary, the graph will not intersect the x-axis.

Can a quadratic equation with b=0 or c=0 have more than one solution?

If b=0, then the quadratic equation will have only one solution, which is x=0. If c=0, then the quadratic equation can have one or two solutions, depending on the value of b. If b=0, then the equation will have two solutions, x=0 and x=0. If b≠0, then the equation will have one solution, x=0. In general, a quadratic equation can have a maximum of two real solutions.

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